Question

How do you differentiate `f(x) = 4(x^2 + x - 1)^10` using the chain rule?

Answer 1

`f'(x) = 40(x^2 + x -1)^9 * (2x + 1)`

Explanation:

let `u = x^2 + x -1`
now `f(x) = 4u^10`

differentiate:
remember, chain rule requires you to multiply by the derivative of the inside function (or `u'`)
`f'(x) = 4 * 10u^9 * u'`

`f'(x) = 4 * 10(x^2 + x -1)^9 * (x^2 + x -1)'`

`f'(x) = 4 * 10(x^2 + x -1)^9 * (2x + 1)`

`f'(x) = 40(x^2 + x -1)^9 * (2x + 1)`

you might rewrite this as:
`f'(x) = (80x+40)(x^2 + x -1)^9`