Answer
$F'(x)=4(5x^{6}+2x^{3})^{3}(30x^{5}+6x^{2})$
Work Step by Step
$F(x)=(5x^{6}+2x^{3})^{4}$
Differentiate using the chain rule, which is $\dfrac{df(u)}{dx}=\dfrac{df}{du}\dfrac{du}{dx}$:
$F'(x)=4(5x^{6}+2x^{3})^{3}(5x^{6}+2x^{3})'=...$
$...=4(5x^{6}+2x^{3})^{3}(30x^{5}+6x^{2})$
