Differentiation of function with chain rule the following expression is part of a function I have to differentiate:
$y = \tan^3(5x^4-7)$
I tried using the chain-rule, so:
$ y' = 3\tan^2(5x^4-7)\cdot(20x^3)$
is this correct? 

Set $t=5x^4-7,~~~u=\tan(t)$ so, you have $$y=u^3$$. Now use the following routine formulas:
$$\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dt}\cdot\frac{dt}{dx},~~~(\tan (t))'=1+\tan^2(t)$$
