Class 12-commerce RD SHARMA Solutions Maths Chapter 11: Differentiation
Differentiation Exercise Ex. 11.1
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Differentiation Exercise Ex. 11.2
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
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36
Solution 37
Solution 38
Solution 39
Solution 40
Solution 41
Solution 42
Solution 43
Solution 44
Solution 45
Solution 46
Solution 47
Solution 48
Solution 49
Solution 50
Solution 51
Solution 52
Solution 53
Solution 54
Solution 55
Solution 56
Solution 57
Solution 58
Solution 59
Solution 60
Solution 61
Solution 62
Given: 
Differentiating w.r.t x, we get
Hence, 
Solution 63
Solution 64
Solution 65
Solution 66
Solution 67
Solution 68
Solution 69
Solution 70
Solution 71
Solution 72
Solution 73
Solution 74
Solution 75
Given: 
Solution 76
Given: 
Differentiation Exercise Ex. 11.3
Solution 1
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Solution 9
Solution 10
Solution 11
Solution 12
Let 
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
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36
Solution 37(i)
Solution 37(ii)
Solution 38
Solution 39
Solution 40
Solution 41
Solution 42
Solution 43
Solution 44
Solution 45
Solution 46
Solution 47
Solution 48
Given: 
………. (i)
Let 
From (i), we get
Differentiation Exercise Ex. 11.4
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: 
Differentiating w.r.t x. we get
When x =1 and 
we get
Solution 30
Solution 31
Differentiation Exercise Ex. 11.5
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(i)
Solution 18(ii)
Solution 18(iii)
Solution 18(iv)
Solution 18(v)
Solution 18(vi)
Solution 18(vii)
Solution 18(viii)
Solution 19
Solution 20
Solution 21
Solution 22
Solution 23
Solution 24
Solution 25
Solution 26
Solution 27
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)
Solution 29(ii)
Solution 30
Solution 31
Solution 32
Solution 33
Solution 34
Solution 35
Solution 36
Solution 37
Solution 38
Solution 39
Solution 40
Solution 41
Solution 42
Solution 43
Solution 44
Solution 45
Solution 46
Solution 47
Solution 48
Solution 49
Solution 50
Solution 51
Solution 52
Solution 53
Solution 54
Solution 55
Solution 56
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
Solution 2
Solution 3
Solution 4
Solution 5
Solution 6
Solution 7
Solution 8
Differentiation Exercise Ex. 11.7
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: 
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
Solution 3
Solution 4(i)
Solution 4(ii)
Solution 5(i)
Solution 5(ii)
Solution 5(iii)
Solution 6
Solution 7(i)
Solution 7(ii)
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
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
