Derivatives

Short Answer Questions:

1. Find the derivative of

Solution:

Let

2. Find the derivative of .

Solution:

Let

3. Find the derivative of

Solution:

Let,

4. Find the derivative of

Solution:

Let

5. Find the derivative of

Solution:

Let

.

6. Find the derivative of where a, b, c are non-zero constant, by first principle.

Solution:

Given,

7. Find the derivative of from the first principle.

Solution:

Let,

At

8. Find the derivative of from first principle.

Solution:

Let,

9. Find the derivative of from first principle.

Solution:

Let,

Long Answer Questions:

10. Find the first principle the derivative of

Solution:

Let,

.

11. Differentiate with respect to

Solution:

Let,

Alternative method.

12. If , prove that

Solution:

Given,

L.H.S

R.H.S.

Alternative method.

2

2

Hence Proved

13. For the curve , find the slope of the tangent at

Solution:

Given,

At ,

Slope of the tangent to is