**NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex
13.2**

NCERT Solutions for Class
11 Maths Chapter 13
Limits and Derivatives Ex 13.2 are the part of NCERT Solutions for Class 11
Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 13
Limits and Derivatives Ex 13.2.

**Ex 13.2 Class 11 Maths Question 1.**

Find the derivative of x^{2}– 2 at x = 10.

**Solution:**

Let f(x) = x^{2} – 2
…(i)

Differentiating (i) with respect to x, we get

f'(x) = 2x

At x = 10, f'(10) = 2(10) = 20.

**Ex 13.2 Class 11
Maths Question 2.**

Find the derivative of x at x = 1.

**Solution:**

Let f(x) = x …(i)

Differentiating (i) with respect to x, we get

f'(x) = 1

At x = 1, f'(1) = 1.

**Ex 13.2 Class 11
Maths Question 3.**

Find the derivative of 99x at x = 100.

**Solution:**

Let f(x) = 99x …(i)

Differentiating (i) with respect to x, we get

f'(x) = 99

At x = 100, f'(100) = 99.

**Ex 13.2 Class 11 Maths Question
4.**

Find the
derivative of the following functions from first principle.**(i)**x

^{3}– 27

**(ii)**(x – 1) (x – 2)

**(iii)**1/x

^{2}

**(iv)**(x+1)/(x−1)

**Solution:**

**Ex 13.2 Class 11 Maths Question
5.**

For the
functionProve that f'(1) = 100f'(0).

**Solution:**

Given,

**Ex 13.2 Class 11 Maths Question
6.**

Find the derivative of x^{n}+ ax

^{n-1}+ a

^{2}x

^{n-2 }+ …. + a

^{n-1}x + a

^{n}for some fixed real number a.

**Solution:**

Let f(x) = x^{n} + ax^{n-1} + a^{2}x^{n-2 }+
…. + a^{n-1}x + a^{n } …(i)

Differentiating (i) with respect to x, we get

f'(x) = nx^{n-1} + (n – 1)ax^{n-2} + …… + a^{n-1}

**Ex 13.2 Class 11 Maths Question 7.**

For some constants a and b, find the derivative of**(i)**(x – a) (x – b)

**(ii)**(ax

^{2}+ b)

^{2}

**(iii)**(x−a)/(x−b)

**Solution:**

**(i)** Let
f(x) = (x – a) (x – b) ….(1)

Differentiating (1) with respect to x, we get

f'(x) = (x – a) (x – b)’ + (x – a)’ (x – b)

⇒ f'(x) = (x – a) + (x – b) = 2x – a – b

**Ex 13.2 Class 11 Maths Question 8.**

Find the derivative (x^{n}−a

^{n})/(x−a) for some constant a.

**Solution:**

Let f(x) = (x^{n}−a^{n})/(x−a), for some constant a^{ } ….(i)

Differentiating (i) with respect to x, we get

**Ex 13.2 Class 11 Maths Question 9.**

Find the derivative of

**Solution:**

**(i)** Let
f(x) = 2x – 3/4
…(1)

Differentiating (1) with respect to x, we get

f'(x) = 2 – 0 ⇒ f'(x) = 2.

**(ii)** Let
f(x) = (5x^{3} + 3x – 1)(x – 1)

**Ex 13.2 Class 11
Maths Question 10.**

Find the derivative of cos x from first principle.

**Solution:**

Let f(x) = cos x

**Ex 13.2 Class 11
Maths Question 11.**

Find the derivative of the following functions:**(i)**sin x cos x

**(ii)**sec x

**(iii)**5 sec x + 4 cos x

**(iv)**cosec x

**(v)**3 cot x + 5 cosec x

**(vi)**5 sin x – 6 cos x + 7

**(vii)**2 tan x – 7 sec x

**Solution:**

**(i)** Let
f(x) = sin x cos x … (1)

Differentiating (1) with respect to x, we get

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