Answer
y'=96$x^{3}$$(8x^{4}+5)^{2}$
Work Step by Step
The chain rule states that if y=g(h(x)), then y'=g'(h(x))h'(x). Since
y=$(8x^{4}+5)^{3}$, we can set g(x)=$x^{3}$ (outside function) and h(x)=8$x^{4}$+5 (inside function), and use the chain rule to find y'. Therefore,
y'=g'(8$x^{4}$+5)h'(x)
We know that
$\frac{d}{dx}$[$x^{3}$]=3$x^{2}$, using the power rule
$\frac{d}{dx}$[8$x^{4}$+5]=32$x^{3}$, using the power rule
Now that we know that g'(x)=3$x^{2}$ and h'(x)=4$x^{3}$, we can find y'.
y'=3$(8x^{4}+5)^{2}$(32$x^{3}$)
=96$x^{3}$$(8x^{4}+5)^{2}$
