NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 are part of NCERT Solutions for Class 11 Maths. Here we have given NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 11 |

Subject |
Maths |

Chapter |
Chapter 13 |

Chapter Name |
Limits and Derivatives |

Exercise |
Ex 13.2 |

Number of Questions Solved |
11 |

Category |
NCERT Solutions |

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

**Question 1.**

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

**Solution:**

let f(x) = x^{2} – 2

Differentiating (i) with respect to x, we get

f'(x) = 2x

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

**Question 2.**

Find the derivative of 99x at x = 10.

**Solution:**

let f(x) = 99x

Differentiating (i) with respect to x, we get

f'(x) = 90

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

**Question 3.**

Find the derivative of x at x = 10.

**Solution:**

let f(x) = x

Differentiating (i) with respect to x, we get

f'(x) = 1

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

**Question 4.**

Find the derivative of the following functions from first principle.

**(i)** x^{3} – 27

**(ii)** (x – 1)(x – 2)

**(iii)**

**(iv)**

**Solution:**

**Question 5.**

For the function

Prove that f'(1) = 100f'(0)

**Solution:**

We have

**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}

Differentiating (i) with respect to x, we get

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

**Question 7.**

For some constants a and b, find the derivative of

**(i)** (x – a)(x – b)

**(ii)** (ax^{2} + b)^{2}

**(iii)**

**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

**Question 8.**

Find the derivative for some constant a.

**Solution:**

Let f(x) = ….(i), where a is a constant.

Differentiating (i) with respect to x, we get

**Question 9.**

Find the derivative of

**Solution:**

**(i)** Let f(x) = …(1)

Differentiating (i) with respect to x, we get

f'(x) = 2·1 – 0 ⇒ f'(x) = 2.

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

**Question 10.**

Find the derivative of cos x from first principle.

**Solution:**

Let f(x) = cos x

**Question 11.**

Find the derivative of the following functions:

**(i)** sin x cos x

**(ii)** secx

**(iii)** 5 secx + 4 cosx

**(iv)** cosecx

**(v)** 3 cotx + 5 cosecx

**(vi)** 5sinx – 6 cosx + 7

**(vii)** 2 tanx – 7 secx.

**Solution:**

**(i)** Let f(x) = sin x cos x … (1)

Differentiating (1) with respect to x, we get

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