NCERT Class 11-Math's: Chapter –13 Limits and Derivatives Part 3

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Question 9:

Find the derivative of by first principle.

Answer:

By definition

Question 10:

Find the derivative of , by first principle.

Answer:

By definition

Using Binomial theorem, we have

Thus,

Question 12:

Find the derivative of .

Answer:

Let

Differentiating both sides with respect to x, we get

Therefore,

Question 13:

Find the derivative of

Answer:

Let

Differentiating both sides with respect to x, we get

Long Answer Type

Question 14:

Evaluate

Answer:

Note that

Therefore,

Question 15:

Evaluate

Answer:

We have

Question 16:

Evaluate

Answer:

We have