Question

How do you find the derivatives of `f(x) = (2x-3) ^ -2`?

Answer 1

One way to approach this problem is to let
`f(x) = g(h(x))`
where
`g(x) = x^(-2)`
and
`h(x) = 2x-3`

By the Chain Rule
`(df(x))/(dx) = color(red)((d g(h(x)))/(d h(x))) * color(blue)((d h(x))/(dx))`

`= color(red)(-2(h(x))^(-3)) * color(blue)(2)`

`= color(red)(-2(2x-3)^(-3)) * color(blue)(2)`

`= - 4/((2x-3)^3)`