f(x)=(x^5-4/x)^-4
f'(x)=
gave me -4(5x^4-4)/(x^5-4/x)^5 , but its wrong
That does work, but you can also do it by rewriting it first as $\displaystyle 4x^{-1}$ then using the power rule, which gives you $\displaystyle -4x^{-2}$, then changing it back to a fraction to get $\displaystyle -\frac{4}{x^2}$.
By the way, in general, you'll probably want to just commit to memory that the derivative of $\displaystyle \frac{1}{x}$ is $\displaystyle -\frac{1}{x^2}$ since it seems to come up often enough that it will be a time saver to just learn it.