Question

g(z) = (z^6 + (z^2 - 1)^6)^(-3)

find the derivative

Answer 1

use the chain rule

Answer 2

let
\[g(z) = (z^6 + (z^2 - 1)^6)^{-3}=u\]
let
\[z^6 + (z^2 - 1)^6 = y\]

\[\frac{du}{dx} = \frac{du}{dy}\frac{dy}{dx}\]

so find those two derivatives and times them together. this is called the chain rule (as already said above)

Answer 3

\[u = y^{-3}\]