Class 12-science RD SHARMA Solutions Maths Chapter 11 - Differentiation
Differentiation Exercise Ex. 11.1
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/35561_image002.png)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/35581_image004.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/35611_image006.png)
Solution 4
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/35671_11.1a.jpg)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/35681_11.6a.jpg)
Solution 7
Solution 8
Solution 9
Solution 10
Differentiation Exercise Ex. 11.2
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/35771_image023.png)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/35781_image025.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/35791_image027.png)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/35801_image029.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/35811_image031.png)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/35821_image033.png)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/35831_image035.png)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/35841_image037.png)
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/35851_image039.png)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/35871_image041.png)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/35891_image043.png)
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/35911_image045.png)
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/35931_image047.png)
Solution 14
![](https://images.topperlearning.com/topper/bookquestions/35951_image049.png)
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/35961_11.2-15a.jpg)
Solution 16
Solution 17
![](https://images.topperlearning.com/topper/bookquestions/36011_image056.png)
Solution 18
![](https://images.topperlearning.com/topper/bookquestions/36031_11.2-18a.jpg)
Solution 19
![](https://images.topperlearning.com/topper/bookquestions/36041_11.2-19a.jpg)
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/36061_image062.png)
Solution 21
![](https://images.topperlearning.com/topper/bookquestions/36081_image064.png)
Solution 22
![](https://images.topperlearning.com/topper/bookquestions/36101_image066.png)
Solution 23
![](https://images.topperlearning.com/topper/bookquestions/36121_11.2-23a.jpg)
Solution 24
Solution 25
![](https://images.topperlearning.com/topper/bookquestions/36171_image072.png)
Solution 26
![](https://images.topperlearning.com/topper/bookquestions/36181_image074.png)
![](https://images.topperlearning.com/topper/bookquestions/36181_image075.png)
Solution 27
![](https://images.topperlearning.com/topper/bookquestions/36191_image077.png)
Solution 28
![](https://images.topperlearning.com/topper/bookquestions/36201_image079.png)
Solution 29
![](https://images.topperlearning.com/topper/bookquestions/36211_image081.png)
Solution 30
![](https://images.topperlearning.com/topper/bookquestions/36231_image083.png)
Solution 31
![](https://images.topperlearning.com/topper/bookquestions/36241_11.2-31a.jpg)
Solution 32
![](https://images.topperlearning.com/topper/bookquestions/36251_image087.png)
Solution 33
![](https://images.topperlearning.com/topper/bookquestions/36261_image089.png)
Solution 34
![](https://images.topperlearning.com/topper/bookquestions/36271_image091.png)
Solution 35
![](https://images.topperlearning.com/topper/bookquestions/36281_image093.png)
Solution 36
![](https://images.topperlearning.com/topper/bookquestions/36291_image095.png)
Solution 37
![](https://images.topperlearning.com/topper/bookquestions/36301_image097.png)
Solution 38
![](https://images.topperlearning.com/topper/bookquestions/36331_image099.png)
Solution 39
![](https://images.topperlearning.com/topper/bookquestions/36351_11.2-39a.jpg)
Solution 40
![](https://images.topperlearning.com/topper/bookquestions/36381_image103.png)
Solution 41
![](https://images.topperlearning.com/topper/bookquestions/36411_image105.png)
Solution 42
![](https://images.topperlearning.com/topper/bookquestions/36431_image107.png)
Solution 43
![](https://images.topperlearning.com/topper/bookquestions/36471_image109.png)
Solution 44
![](https://images.topperlearning.com/topper/bookquestions/36491_image111.png)
Solution 45
![](https://images.topperlearning.com/topper/bookquestions/36511_image113.png)
![](https://images.topperlearning.com/topper/bookquestions/36511_image114.png)
![](https://images.topperlearning.com/topper/bookquestions/36511_image115.png)
Solution 46
![](https://images.topperlearning.com/topper/bookquestions/36521_image117.png)
Solution 47
![](https://images.topperlearning.com/topper/bookquestions/36531_image119.png)
Solution 48
![](https://images.topperlearning.com/topper/bookquestions/36541_11.2-48a.jpg)
Solution 49
![](https://images.topperlearning.com/topper/bookquestions/197273_11.2-49a.jpg)
Solution 50
![](https://images.topperlearning.com/topper/bookquestions/197275_11.2-50a.jpg)
Solution 51
![](https://images.topperlearning.com/topper/bookquestions/197277_11.2-51a.jpg)
Solution 52
![](https://images.topperlearning.com/topper/bookquestions/197279_11.2-52a.jpg)
Solution 53
Solution 54
![](https://images.topperlearning.com/topper/bookquestions/197283_11.2-54a.jpg)
Solution 55
![](https://images.topperlearning.com/topper/bookquestions/197285_11.2-55a.jpg)
Solution 56
![](https://images.topperlearning.com/topper/bookquestions/197287_11.2-56a.jpg)
Solution 57
![](https://images.topperlearning.com/topper/bookquestions/197289_11.2-57a.jpg)
Solution 58
![](https://images.topperlearning.com/topper/bookquestions/197291_11.2-58a.jpg)
Solution 59
![](https://images.topperlearning.com/topper/bookquestions/197293_11.2-59a.jpg)
Solution 60
![](https://images.topperlearning.com/topper/bookquestions/197295_11.2-60a.jpg)
Solution 61
![](https://images.topperlearning.com/topper/bookquestions/197297_11.2-61a.jpg)
Solution 62
Given:
Differentiating w.r.t x, we get
Hence,
Solution 63
![](https://images.topperlearning.com/topper/bookquestions/36641_11.2-63a.jpg)
Solution 64
![](https://images.topperlearning.com/topper/bookquestions/36651_image153.png)
Solution 65
![](https://images.topperlearning.com/topper/bookquestions/36661_11.2-65a.jpg)
Solution 66
![](https://images.topperlearning.com/topper/bookquestions/36731_image158.png)
Solution 67
![](https://images.topperlearning.com/topper/bookquestions/36741_image160.png)
Solution 68
![](https://images.topperlearning.com/topper/bookquestions/36751_image162.png)
Solution 69
![](https://images.topperlearning.com/topper/bookquestions/36771_image164.png)
Solution 70
![](https://images.topperlearning.com/topper/bookquestions/36791_image166.png)
Solution 71
![](https://images.topperlearning.com/topper/bookquestions/36801_image168.png)
Solution 72
![](https://images.topperlearning.com/topper/bookquestions/36811_image170.png)
Solution 73
![](https://images.topperlearning.com/topper/bookquestions/36821_11.2-73a.jpg)
Solution 74
![](https://images.topperlearning.com/topper/bookquestions/36851_image174.png)
![](https://images.topperlearning.com/topper/bookquestions/36851_image175.png)
Solution 75
Given:
Solution 76
Given:
Differentiation Exercise Ex. 11.3
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/36881_image177.png)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/36921_11.3-2a.jpg)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/36931_11.3-3a.jpg)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/36941_image183.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/36951_11.3-5a.jpg)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/36961_image187.png)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/36971_image189.png)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/36991_image191.png)
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/37021_11.3-9a.jpg)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/37031_image195.png)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/37041_image197.png)
Solution 12
Let
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/37061_11.3-13.jpg)
Solution 14
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/37081_11.3-15a.jpg)
Solution 16
![](https://images.topperlearning.com/topper/bookquestions/37171_image207.png)
Solution 17
![](https://images.topperlearning.com/topper/bookquestions/37181_image209.png)
Solution 18
![](https://images.topperlearning.com/topper/bookquestions/37201_image211.png)
Solution 19
![](https://images.topperlearning.com/topper/bookquestions/37221_image213.png)
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/37241_image215.png)
Solution 21
![](https://images.topperlearning.com/topper/bookquestions/99051_la11.gif)
Solution 22
![](https://images.topperlearning.com/topper/bookquestions/37261_image217.png)
Solution 23
![](https://images.topperlearning.com/topper/bookquestions/37271_image219.png)
Solution 24
![](https://images.topperlearning.com/topper/bookquestions/37281_image221.png)
Solution 25
![](https://images.topperlearning.com/topper/bookquestions/37291_image223.png)
Solution 26
![](https://images.topperlearning.com/topper/bookquestions/37301_11.3-26a.jpg)
Solution 27
![](https://images.topperlearning.com/topper/bookquestions/37311_11.3-27a.jpg)
Solution 28
![](https://images.topperlearning.com/topper/bookquestions/37351_image229.png)
Solution 29
![](https://images.topperlearning.com/topper/bookquestions/37361_image231.png)
Solution 30
![](https://images.topperlearning.com/topper/bookquestions/37421_image233.png)
Solution 31
![](https://images.topperlearning.com/topper/bookquestions/37451_image235.png)
Solution 32
![](https://images.topperlearning.com/topper/bookquestions/37481_image237.png)
Solution 33
![](https://images.topperlearning.com/topper/bookquestions/37521_image239.png)
Solution 34
![](https://images.topperlearning.com/topper/bookquestions/99081_la33.gif)
Solution 35
Solution 36
![](https://images.topperlearning.com/topper/bookquestions/37551_image243.png)
Solution 37(i)
![](https://images.topperlearning.com/topper/bookquestions/99071_la22.gif)
Solution 37(ii)
![](https://images.topperlearning.com/topper/bookquestions/37691_11.3-37ii.jpg)
Solution 38
Solution 39
![](https://images.topperlearning.com/topper/bookquestions/37611_11.3-39a.jpg)
Solution 40
![](https://images.topperlearning.com/topper/bookquestions/37621_image250.png)
Solution 41
![](https://images.topperlearning.com/topper/bookquestions/37631_image252.png)
![](https://images.topperlearning.com/topper/bookquestions/37631_image253.png)
Solution 42
![](https://images.topperlearning.com/topper/bookquestions/37641_image255.png)
Solution 43
![](https://images.topperlearning.com/topper/bookquestions/37651_11.3-43a.jpg)
Solution 44
![](https://images.topperlearning.com/topper/bookquestions/37661_11.3-44a.jpg)
Solution 45
Solution 46
![](https://images.topperlearning.com/topper/bookquestions/37701_image265.png)
Solution 47
Solution 48
Given: ………. (i)
Let
From (i), we get
Differentiation Exercise Ex. 11.4
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/37801_image267.png)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/37821_image269.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/37831_image271.png)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/37861_image273.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/37881_image275.png)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/37901_image277.png)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/37911_image279.png)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/37931_image281.png)
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/37961_11.4-9a.jpg)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/37971_image285.png)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/37991_11.4-11a.jpg)
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/38001_image289.png)
Solution 13
Solution 14
![](https://images.topperlearning.com/topper/bookquestions/38031_image293.png)
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/38041_image295.png)
Solution 16
![](https://images.topperlearning.com/topper/bookquestions/38051_image297.png)
Solution 17
![](https://images.topperlearning.com/topper/bookquestions/38061_image299.png)
Solution 18
![](https://images.topperlearning.com/topper/bookquestions/38081_image301.png)
Solution 19
![](https://images.topperlearning.com/topper/bookquestions/38091_11.4-19a.jpg)
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/38101_image305.png)
Solution 21
![](https://images.topperlearning.com/topper/bookquestions/38131_image307.png)
![](https://images.topperlearning.com/topper/bookquestions/38131_image308.png)
Solution 22
![](https://images.topperlearning.com/topper/bookquestions/38141_11.4-22a.jpg)
Solution 23
![](https://images.topperlearning.com/topper/bookquestions/38181_image312.png)
Solution 24
![](https://images.topperlearning.com/topper/bookquestions/38201_image314.png)
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Given:
Differentiating w.r.t x. we get
When x =1 and we get
Solution 30
Solution 31
Differentiation Exercise Ex. 11.5
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/41821_11.5-1.jpg)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/41831_image329.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/41891_11.5-3a.jpg)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/42011_image333.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/42031_image335.png)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/42051_image337.png)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/42111_image339.png)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/42121_image341.png)
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/42151_image343.png)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/42161_image345.png)
Solution 11
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/42171_image347.png)
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/42181_image349.png)
Solution 14
![](https://images.topperlearning.com/topper/bookquestions/42191_image351.png)
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/42211_image353.png)
Solution 16
![](https://images.topperlearning.com/topper/bookquestions/42221_image355.png)
Solution 17
![](https://images.topperlearning.com/topper/bookquestions/42251_11.5-17a.jpg)
Solution 18(i)
![](https://images.topperlearning.com/topper/bookquestions/42271_11.5-18.1.jpg)
Solution 18(ii)
![](https://images.topperlearning.com/topper/bookquestions/42281_image361.png)
Solution 18(iii)
Solution 18(iv)
Solution 18(v)
Solution 18(vi)
![](https://images.topperlearning.com/topper/bookquestions/42291_image363.png)
Solution 18(vii)
![](https://images.topperlearning.com/topper/bookquestions/42301_image365.png)
Solution 18(viii)
Solution 19
![](https://images.topperlearning.com/topper/bookquestions/42311_image367.png)
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/42321_image369.png)
Solution 21
![](https://images.topperlearning.com/topper/bookquestions/42331_11.5-21a.jpg)
Solution 22
![](https://images.topperlearning.com/topper/bookquestions/42341_image373.png)
Solution 23
![](https://images.topperlearning.com/topper/bookquestions/42351_image375.png)
Solution 24
![](https://images.topperlearning.com/topper/bookquestions/42361_11.5-24a.jpg)
Solution 25
![](https://images.topperlearning.com/topper/bookquestions/88491_11.5-25a.jpg)
Solution 26
![](https://images.topperlearning.com/topper/bookquestions/42371_image379.png)
Solution 27
![](https://images.topperlearning.com/topper/bookquestions/42381_image381.png)
Solution 28
Given:
Let
Differentiating 'u' w.r.t x, we get
Differentiating 'v' w.r.t x, we get
From (i), (ii) and (iii), we get
Solution 29(i)
![](https://images.topperlearning.com/topper/bookquestions/42561_image385.png)
Solution 29(ii)
![](https://images.topperlearning.com/topper/bookquestions/42641_image387.png)
Solution 30
![](https://images.topperlearning.com/topper/bookquestions/42681_image389.png)
Solution 31
![](https://images.topperlearning.com/topper/bookquestions/42701_image391.png)
Solution 32
Solution 33
![](https://images.topperlearning.com/topper/bookquestions/42711_image393.png)
Solution 34
![](https://images.topperlearning.com/topper/bookquestions/42721_11.5-34a.jpg)
Solution 35
![](https://images.topperlearning.com/topper/bookquestions/42751_image397.png)
Solution 36
Solution 37
Solution 38
![](https://images.topperlearning.com/topper/bookquestions/42821_11.5-38a.jpg)
Solution 39
![](https://images.topperlearning.com/topper/bookquestions/42831_11.5-39a.jpg)
Solution 40
![](https://images.topperlearning.com/topper/bookquestions/42851_image407.png)
Solution 41
![](https://images.topperlearning.com/topper/bookquestions/42881_image409.png)
Solution 42
![](https://images.topperlearning.com/topper/bookquestions/42921_11.5-42a.jpg)
Solution 43
![](https://images.topperlearning.com/topper/bookquestions/42941_image413.png)
Solution 44
![](https://images.topperlearning.com/topper/bookquestions/42961_image415.png)
Solution 45
![](https://images.topperlearning.com/topper/bookquestions/42991_image417.png)
Solution 46
![](https://images.topperlearning.com/topper/bookquestions/196573_11.5-46a.jpg)
Solution 47
![](https://images.topperlearning.com/topper/bookquestions/196575_11.5-47a.jpg)
Solution 48
![](https://images.topperlearning.com/topper/bookquestions/43611_image421.png)
Solution 49
![](https://images.topperlearning.com/topper/bookquestions/43631_11.5-49a.jpg)
Solution 50
![](https://images.topperlearning.com/topper/bookquestions/43641_image425.png)
Solution 51
![](https://images.topperlearning.com/topper/bookquestions/43661_image427.png)
Solution 52
![](https://images.topperlearning.com/topper/bookquestions/43681_image429.png)
Solution 53
![](https://images.topperlearning.com/topper/bookquestions/43711_11.5-53a.jpg)
Solution 54
Solution 55
![](https://images.topperlearning.com/topper/bookquestions/116851_11.5-55a.jpg)
Solution 56
![](https://images.topperlearning.com/topper/bookquestions/196571_11.5-56a.jpg)
Solution 57
Solution 58
Solution 59
Solution 60
Solution 61
Solution 62
Given:
Let
Taking log on both the sides of equation (i), we get
Taking log on both the sides of equation (ii), we get
Differentiating (iii) w.r.t x, we get
Using (iv) and (v), we have
Differentiation Exercise Ex. 11.6
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/43791_11.6-1a.jpg)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/43831_image436.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/43841_image438.png)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/43851_image440.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/43861_11.6-5a.jpg)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/43881_image444.png)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/43931_image446.png)
![](https://images.topperlearning.com/topper/bookquestions/43931_image447.png)
Solution 8
Differentiation Exercise Ex. 11.7
Solution 1
![](https://images.topperlearning.com/topper/bookquestions/99151_la44.gif)
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/44221_image451.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/88641_11.7-3.jpg)
Solution 4
![](https://images.topperlearning.com/topper/bookquestions/44231_image453.png)
Solution 5
![](https://images.topperlearning.com/topper/bookquestions/44241_11.7-5a.jpg)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/88651_11.7-6a.jpg)
Solution 7
![](https://images.topperlearning.com/topper/bookquestions/44251_11.7-7a.jpg)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/44261_image459.png)
![](https://images.topperlearning.com/topper/bookquestions/44261_image460.png)
Solution 9
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/44271_image462.png)
![](https://images.topperlearning.com/topper/bookquestions/44271_image463.png)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/44281_image465.png)
![](https://images.topperlearning.com/topper/bookquestions/44281_image466.png)
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/44291_11.7-12a.jpg)
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/44301_image471.png)
![](https://images.topperlearning.com/topper/bookquestions/44301_image472.png)
Solution 14
![](https://images.topperlearning.com/topper/bookquestions/44311_11.7-14a.jpg)
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/44321_image477.png)
Solution 16
![](https://images.topperlearning.com/topper/bookquestions/44331_image479.png)
Solution 17
Solution 18
Solution 19
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/44361_image485.png)
Solution 21
![](https://images.topperlearning.com/topper/bookquestions/44371_image487.png)
![](https://images.topperlearning.com/topper/bookquestions/44371_image488.png)
Solution 22
Solution 23
![](https://images.topperlearning.com/topper/bookquestions/196801_11.7-23a.jpg)
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Given:
Differentiate 'x'
w.r.t , we get
Differentiate 'y'
w.r.t , we get
Dividing (ii) by (i), we get
At
Differentiation Exercise Ex. 11.8
Solution 1
We need to find
Let
So, we need to
find
Solution 2
![](https://images.topperlearning.com/topper/bookquestions/44391_image492.png)
Solution 3
![](https://images.topperlearning.com/topper/bookquestions/44401_11.8-3a.jpg)
Solution 4(i)
![](https://images.topperlearning.com/topper/bookquestions/44411_image496.png)
Solution 4(ii)
Solution 5(i)
Solution 5(ii)
![](https://images.topperlearning.com/topper/bookquestions/44441_image503.png)
Solution 5(iii)
![](https://images.topperlearning.com/topper/bookquestions/44451_image505.png)
![](https://images.topperlearning.com/topper/bookquestions/44451_image506.png)
Solution 6
![](https://images.topperlearning.com/topper/bookquestions/44461_11.8-6a.jpg)
Solution 7(i)
![](https://images.topperlearning.com/topper/bookquestions/44471_11.8-7i.jpg)
Solution 7(ii)
![](https://images.topperlearning.com/topper/bookquestions/44481_11.8-7ii.jpg)
Solution 8
![](https://images.topperlearning.com/topper/bookquestions/44491_image517.png)
Solution 9
![](https://images.topperlearning.com/topper/bookquestions/44501_image519.png)
![](https://images.topperlearning.com/topper/bookquestions/44501_image520.png)
Solution 10
![](https://images.topperlearning.com/topper/bookquestions/44511_image522.png)
![](https://images.topperlearning.com/topper/bookquestions/44511_image523.png)
Solution 11
![](https://images.topperlearning.com/topper/bookquestions/44521_image525.png)
![](https://images.topperlearning.com/topper/bookquestions/44521_image526.png)
Solution 12
![](https://images.topperlearning.com/topper/bookquestions/44531_image528.png)
![](https://images.topperlearning.com/topper/bookquestions/44531_image529.png)
Solution 13
![](https://images.topperlearning.com/topper/bookquestions/44541_11.8-13a.jpg)
Solution 14
![](https://images.topperlearning.com/topper/bookquestions/44551_image534.png)
![](https://images.topperlearning.com/topper/bookquestions/44551_image535.png)
Solution 15
![](https://images.topperlearning.com/topper/bookquestions/44561_image537.png)
![](https://images.topperlearning.com/topper/bookquestions/44561_image538.png)
Solution 16
![](https://images.topperlearning.com/topper/bookquestions/44571_image540.png)
![](https://images.topperlearning.com/topper/bookquestions/44571_image541.png)
Solution 17
![](https://images.topperlearning.com/topper/bookquestions/44581_image543.png)
![](https://images.topperlearning.com/topper/bookquestions/44581_image544.png)
Solution 18
![](https://images.topperlearning.com/topper/bookquestions/44591_image546.png)
![](https://images.topperlearning.com/topper/bookquestions/44591_image547.png)
Solution 19
![](https://images.topperlearning.com/topper/bookquestions/44601_image549.png)
![](https://images.topperlearning.com/topper/bookquestions/44601_image550.png)
Solution 20
![](https://images.topperlearning.com/topper/bookquestions/44611_11.8-20a.jpg)
Solution 21
We need to find
Let
Differentiating 'u' and 'v' w.r.t x, we get
Dividing (i) by (ii), we get
Differentiation Exercise MCQ
Solution 1
Correct option: (d)
Solution 2
Correct option: (c)
Solution 3
Correct option: (a)
Solution 4
Correct option: (d)
Solution 5
Correct option: (d)
Solution 6
Correct option: (a)
Solution 7
Correct option: (d)
Solution 8
Correct option: (c)
Solution 9
Correct option: (d)
Solution 10
Correct option:(a)
Solution 11
Correct option: (a)
Solution 12
Correct option: (c)
Solution 13
Correct option: (d)
Solution 14
Correct option: (d)
Solution 15
Correct option: (b)
Solution 16
Correct option: (a)
Solution 17
Correct option: (d)
Solution 18
Correct option: (a)
Solution 19
Correct option: (b)
Solution 20
Correct option: (a)
Solution 21
Correct option: (b)
Solution 22
Correct option: (c)
Solution 23
Correct option:(d)
Solution 24
Correct option: (a)
Solution 25
Correct option: (b)
Solution 26
Correct option: (c)
Solution 27
Correct option:(a)
Solution 28
Correct option: (b)
Solution 29
Correct option: (b)
Solution 30
Correct option: (a)
Solution 31
Correct option: (b)
Solution 32
Correct option: (c)
Solution 33
Given:
Differentiating w.r.t x, we get
Differentiation Exercise Ex. 11VSAQ
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Solution 17
Solution 18
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
Solution 28
Solution 29
Given:
Solution 30
Given: f(x) = x + 7 and g(x) = x - 7
Now, (fog)(x) = f(g(x)) = f(x - 7) = x - 7 + 7 = x
Therefore, (fog)(x) = x