Question

Find f'(x) if f(x) = (2/(x^1/3)) + 3 cos x + x^pi

Answer 1

The derivative of $f$ is

$f'(x)=\left(2x^{-1/3}+3\cos x+x^\pi\right)'$

$f'(x)=\left(2x^{-1/3}\right)'+(3\cos x)'+\left(x^\pi\right)'$

By the power rule,

$f'(x)=-\dfrac23x^{-4/3}+(3\cos x)'+\pi x^{\pi-1}$

The derivative of $\cos x$ is $-\sin x$:

$f'(x)=-\dfrac23x^{-4/3}-3\sin x+\pi x^{\pi-1}$