KC Sinha Mathematics Solution Class 11 Chapter 29 Derications and Rules of Differentiation Exercise 29.2

 Exercise 29.2

Page no 29.25 

Type 1 

Question 1

Find the differential coefficients of the following from first principle :

1. (i) $x^{3}$ (ii) $5 x^{4}$

2. (i) $\frac{1}{x}$

(ii) $\frac{1}{x^{2}}$

(iii) $(-x)^{-1}$

3. $\frac{1}{\sqrt{2 x}}$

Question 4

(i) $\sqrt{2 x-a}$

(ii) $\sqrt{x}$

Question 5

(i) $x^{8}+x^{3}$

(ii) $x^{3}+3 x^{2}+5$

(iii) $(x-1)(x-2)$

(iv) $x^{3}-27$

(v) $x+\frac{1}{x}$

Question 6

(i) $\frac{x+1}{x-1}$

(ii) $\frac{2 x+3}{x-2}$

Type 2

Question 7

$\sin 4 x$

Question 8

$\cos 2 x$

Question 9

$\tan 2 x$

Question 10

$\tan k x$

Question 11

$\sin a x$

Question 12

$\sec (2 x+3)$

Question 13

$\tan \frac{x^{\circ}}{2}$

Question 14

$\sin x^{\circ}$

Question 15

$\cos ^{2} x$

Question 16

 $\cos x^{2}$

Question 17

$\sin \left(x^{2}+2\right)$

Question 18

$\sin ^{3} x$

Question 19

$\sqrt{\tan x}$

Question 20

. $x^{2} \cos x$

Question 21

 (i) $\cos (3 x+2)$

(ii) $\cos \left(x-\frac{\pi}{8}\right)$

Question 22

 (i) $\sin (x+1)$

(ii) $\sin (2 x+1)$

Question 23

 $\cos ^{3} x$

Question 24

 $\tan (a x+b)$

Question 25

$x \sin x$

Question 26

 $\sqrt{\cos x}$

Question 27

$\sqrt{\sec x}$

Question 28

 $\sqrt{\sin 3 x}$

Question 29

 $\sin \left(x^{2}+1\right)$

Question 30

 $\tan \left(x^{2}+1\right)$

Question 31

 $\cos \sqrt{x}$

Question 32

 $\frac{\cos x}{x}$

Question 33

$\sin x+\cos x$