Examples on Chain Rule

Example 10.8

Find F′(x) if F (x) = √[x² +1]

Solution

Take u = g(x) = x² + 1 and f (u) =√u

∴ F (x) = ( fog)(x) = f (g(x))

Example 10.9

Differentiate : (i) y = sin(x²) (ii) y = sin²x

Solution

(i) The outer function is the sine function and the inner function is the squaring function.

Let u = x²

That is, y = sin u.

EXERCISE 10.3

Differentiate the following :