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

## Differentiation Exercise Ex. 11.1

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## Differentiation Exercise Ex. 11.2

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Given:

Differentiating w.r.t x, we get

Hence,

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Given:

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Given:

## Differentiation Exercise Ex. 11.3

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Let

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### Solution 37(i)

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Given: ………. (i)

Let

From (i), we get

## Differentiation Exercise Ex. 11.4

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Given:

Differentiating w.r.t x. we get

When x =1 and we get

### Solution 30

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## Differentiation Exercise Ex. 11.5

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### Solution 18(i)

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### Solution 18(iii)

### Solution 18(iv)

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### Solution 18(vi)

### Solution 18(vii)

### Solution 18(viii)

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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)

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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

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## Differentiation Exercise Ex. 11.7

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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

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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)

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Correct option: (c)

### Solution 13

Correct option: (d)

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Correct option: (d)

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Correct option: (b)

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Correct option: (a)

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Correct option: (d)

### Solution 18

Correct option: (a)

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Correct option: (b)

### Solution 20

Correct option: (a)

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Correct option: (b)

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Correct option: (c)

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Correct option:(d)

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Correct option: (a)

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Correct option: (b)

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Correct option: (c)

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Correct option:(a)

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Correct option: (b)

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Correct option: (b)

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Correct option: (a)

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Correct option: (b)

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Correct option: (c)

### Solution 33

Given:

Differentiating w.r.t x, we get

## Differentiation Exercise Ex. 11VSAQ

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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