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 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 x2 – 2 at x = 10.

Solution:
Let f(x) = x2 – 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) x3 – 27
(ii) (x – 1) (x – 2)
(iii) 1/x2
(iv) (x+1)/(x1)

Solution:


Ex 13.2 Class 11 Maths Question 5.

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

Solution:
Given,


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         …(i)
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) (xa)/(xb)

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 (xnan)/(xa) for some constant a.

Solution:
Let f(x) = (xnan)/(xa), 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) = (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) 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

 

You can also like these:

NCERT Solutions for Maths Class 9

NCERT Solutions for Maths Class 10

NCERT Solutions for Maths Class 12

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