Answer
The derivative is $\frac{-2}{3x\sqrt[3] x}-3sin(x)$.
Work Step by Step
To find $f'(x)$ just apply the power rule $((x^n)'=nx^{n-1})$ to the terms that make up the function as follows after rewriting as $f(x)=2x^{-\frac{1}{3}}+3cos(x)$
$f'(x)=(2x^{-\frac{1}{3}}+3cos(x))'=(2x^{-\frac{1}{3}})'+(3cos(x))'=$
$(2)(-\frac{1}{3})(x^{-\frac{1}{3}-1})+(3)(-sin(x))=\frac{-2}{3x\sqrt[3] x}-3sin(x)$
