Answer
$f'(x) = (30x^2+45)(2x^3+9x)^4$
Work Step by Step
In order to derivate this function you have to apply the chain rule
Let's make a «u» substitution to make it easier
$u = 2x^3+9x$
$f(u) = u^5$
Derivate the function:
$f'(u) = 5u^4u'$
Now let's find u'
$u' = 6x^2+9$
Then undo the substitution, simplify and get the answer:
$f'(x) = 5(6x^2+9)(2x^3+9x)^4$
$f'(x) = (30x^2+45)(2x^3+9x)^4$
