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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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