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

Here, Below you all know about NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives Ex 13.2 Question Answer. I know many of you confuse about finding Chapter 13 Limits and Derivatives Ex 13.2 Of Class 11 NCERT Solutions. So, Read the full post below and get your solutions.

TextbookNCERT
BoardCBSE
CategoryNCERT Solutions
ClassClass 11
SubjectMaths
ChapterChapter 13
ExerciseClass 11 Maths Chapter 13 Limits and Derivatives Exercise 13.2
Number of Questions Solved11
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

NCERT TEXTBOOK EXERCISES

Ex 13.2 Class 11 Maths Question 1.
Find the derivative of x2 – 2 at x = 10.

Solution:

let f(x) = x2 – 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) x3 – 27
(ii) (x – 1)(x – 2)
(iii) 1/x2
(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 xn + axn-1 + a2xn-2+
…. + an-1x + an for some fixed real number a.

Solution:

Let f(x) = xn + axn-1 + a2xn-2+
…. + an-1x + an
Differentiating (i) with respect to x, we get
f'(x) = nxn-1 + (n – 1)axn-2 + …… + an-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) (ax2 + 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) = 5x3 + 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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