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# Class 12-science RD SHARMA Solutions Maths Chapter 11 - Differentiation

## Differentiation Exercise Ex. 11.2

### Solution 62

Given:

Differentiating w.r.t x, we get

Hence,

Given:

Given:

Let

Given: ………. (i)

Let

From (i), we get

## Differentiation Exercise Ex. 11.4

### Solution 29

Given:

Differentiating w.r.t x. we get

When x =1 and  we get

## Differentiation Exercise Ex. 11.5

### 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 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. 11.7

### 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 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

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