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

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 11 |

Subject | Maths |

Chapter | Chapter 13 |

Exercise | Class 11 Maths Chapter 13 Limits and Derivatives Exercise 13.2 |

Number of Questions Solved | 11 |

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

**NCERT TEXTBOOK EXERCISES**

**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

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 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.

**Ex 13.2 Class 11 Maths 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.

**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)** $\frac { x+1 }{ x-1 }$

**Solution:**

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

For the function

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

**Solution:**

We have

**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}

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)** $\frac { x-a }{ x-b }$

**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 $\frac { { x }^{ n }-{ a }^{ n } }{ x-a }$ for some constant a.

**Solution:**

Let f(x) = $\frac { { x }^{ n }-{ a }^{ n } }{ x-a }$ ….(i), where a is a constant.

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 (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)

**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)** 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

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

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