# 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