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# NCERT Solutions class-11 Maths Exercise 13.2

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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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