Question

What is the derivative of (x-1)^2 (x+2)?

Answer 1

`3(x^2-1)`

Explanation:

`y=(x-1)^2(x+2)`
using the product rule:
`(uv)'= uv'+vu'`
let: `u=(x-1)^2, v=x+2`:
`dy/dx=(x-1)^2*1+2(x-1)*(x+2)`
`dy/dx=(x-1)[(x-1)+2(x+2)]`
`dy/dx=(x-1)(x-1+2x+4)`
`dy/dx=(x-1)(3x+3)`
`dy/dx=3(x^2-1)`