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:
=