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 :
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 :
