Answer to Question #110075 in Calculus for Nimra

Question

Given f (x²) =x²sinx², compute the derivative of f with respect to x.

Answer 1

As $f(x^2)=x^2sinx^2$

$\frac{d(f(x^2))}{dx}=\frac{d(x^2sinx^2)}{dx}$

$2xf'(x^2)=2xsinx^2+2x^3cosx^2$

Hence, $f'(x^2)=sinx^2+x^2cosx^2$