Question

How do you differentiate `f(x) = (2x-3) ^ -2`?

Answer 1

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

Explanation:

differentiate using the `color(blue)" chain rule "`

`d/dx [f(g(x)) ] = f'(g(x)) . g'(x)`
`"----------------------------------------------"`

f(g(x)) `=(2x-3)^(-2) rArr f'(g(x)) = -2(2x-3)^(-3)`

and g(x) = 2x - 3 → g'(x) = 2
`"----------------------------------------------"`
Substitute these values into the derivative

`rArr f'(x) = -2(2x-3)^(-3)xx2 = (-4)/(2x-3)^3`