# NCERT Class 12-Mathematics: Chapter –5 Continuity and Differentiability Part 13

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**Question 23:**

Show that is continuous but not differentiable at .

**Answer:**

We have

For continuity at ,

Hence, is continuous at .

Now,

So, is not differentiable at .

**Question 24:**

A function satisfies the equation for all , . Suppose that the function is differentiable at and . Prove that .

Differentiate each of the following w.r.t. (Exercises 25 to 43):

**Answer:**

Let satisfies the equation

Let is differentiable at and

Also,

**Question 25:**

Differentiate each of the following w.r.t.

**Answer:**

**Question 26:**

Differentiate each of the following w.r.t. x

**Answer:**

**Question 27:**

**Answer:**

**Question 28:**

**Answer:**

**Question 29:**

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**Question 30:**

**Answer:**

**Question 31:**

**Answer:**