__Example 1__**:**

Differentiate with respect to using chain rule method.

Let us consider , then . Applying chain rule, we have

__Example 2__**:**

Differentiate with respect to using chain rule method.

If , then we have to find . By chain rule method

First we differentiate the function with respect to .

Now differentiate the function with respect to .

Now using the chain rule of differentiation, we have