Limits and Derivatives Miscellaneous
Miscellaneous Exercise
1. Find the derivative of following functions from first principle:
(i)
(ii)
(iii)
(iv)
Ans. (i)Given:
then
= 
= 
= 
(ii)Given:
then
= 
= 
= 
(iii)Given:
then
= 
= 
= 
(iv)Given:
then
= 
= 
= 
Find the derivative of the following functions (it is to be understood that 
and 
are fixed non-zero constants and 
and 
are integers).
2.
Ans. Given:
= 1
3.
Ans. Given:
= 
= 
= 
4.
Ans. Given:
= 
5.
Ans. Given:
= 
= 
6.
Ans. Given:
= 
= 
= 
7.
Ans. Given:
= 
8.
Ans. Given:
9.
Ans. Given:
10.
Ans. Given:
= 
11.
Ans. Given:
= 
12.
Ans. Given:
= 
= 
13.
Ans. Given:
14.
Ans. Given:
= 
15.
Ans. Given:
= 
16.
Ans. Given:
= 
= 
= 
17.
Ans. Given:
18.
Ans. Given:
19.
Ans. Given:
= 
20.
Ans. Given:
= 
21.
Ans. Given:
= 
= 
22.
Ans. Given:
23.
Ans. Given:
= 
24.
Ans. Given:
25.
Ans. Given:
26.
Ans. Given:
27.
Ans. Given:
= 
28.
Ans. Given:
= 
29.
Ans. Given:
30.
Ans. Given:
= 
= 
= 