Exercise 13.2
1. Find the derivative of 
at 
Ans. Here 
Therefore, Derivative of at 
is 
2. Find the derivative of 
at 
Ans. Here 
Therefore, Derivative of at 
is 99
3. Find the derivative of 
at 
Ans. Here 
Therefore, Derivative of at 
is 1
4. Find the derivatives of the following functions from first principle:
(i) 
(ii) 
(iii) 
(iv) 
Ans. (i) Given:
Now, since 
= 
= 
(ii) Given:
Now, since
= 
(iii) Given:
Now, since
= 
= 
= 
= 
(iv) 
Now, since
= 
= 
= 
5. For the function 
prove that 
Ans. Given: 
= 
= 
= 
Now 
And 
Now 
100 = 100 Proved.
6. Find the derivative of 
for some fixed real number 
Ans. Given: 
= 
= 
= 
7. For some constants 
and 
find the derivative of:
(i) 
(ii) 
(iii) 
Ans. (i) Given:
= 
= 
(ii) Given:
= 
= 
= 
= 
= 
(iii) Given:
= 
= 
= 
8. Find the derivative of 
for some constant
Ans. Given:
= 
= 
9. Find the derivative of:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Ans. (i) Given:
= 
(ii) Given:
= 
= 
= 
= 
(iii) Given:
= 
= 
= 
(iv) Given:
= 
= 
= 
(v) Given:
= 
= 
= 
(vi) Given:
= 
= 
= 
= 
10. Find the derivative of 
from first principle.
Ans. Given: 
,
then 
Since, 
= 
= 
= 
11. Find the derivative of the following functions:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
Ans. (i) Given: 
= 
= 
= 
(ii) Given: 
(iii) Given: 
= 
(iv) Given: 
(v) Given: 
= 
(vi) Given: 
= 
= 
(vii) Given: 
= 
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