Question

Given f³ (x) = x²sin(x²), compute the derivative of f with respect to x.

Answer 1

$f^{3}(x)=x^{2}\sin(x^{2}) \\ \implies f(x)=(x^{2}\sin(x^{2}))^{\frac{1}{3}} \\ \implies f^{\prime}(x)=\frac{1}{3}(x^{2}\sin(x^{2}))^{\frac{-2}{3}}. \\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ . \ [2x \sin(x^{2}) +2x^{3} \cos(x^{2})]$