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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