Answer
y'=12$x^{3}$$(x^{4}+5)^{2}$
Work Step by Step
The chain rule states that if y=g(h(x)), then y'=g'(h(x))h'(x). Since
y=$(x^{4}+5)^{3}$, we can set g(x)=$x^{3}$ and h(x)=$x^{4}$+5, and use the chain rule to find y'. Therefore,
y'=g'($x^{4}$+5)h'(x)
We know that
$\frac{d}{dx}$[$x^{3}$]=3$x^{2}$, using the power rule
$\frac{d}{dx}$[$x^{4}$+5]=4$x^{3}$, using the power rule
Now that we know that g'(x)=3$x^{2}$ and h'(x)=4$x^{3}$, we can find y'.
y'=3$(x^{4}+5)^{2}$(4$x^{3}$)
=12$x^{3}$$(x^{4}+5)^{2}$
