Question

How do you find the derivative of `x(x-4)^3`?

Answer 1

`d/dx [x(x-4)^3] = 4(x-4)^2 (x-1)`

Explanation:

Using the product rule:

`d/dx [x(x-4)^3] = x d/dx [(x-4)^3]+ [d/dx (x)] (x-4)^3`

`d/dx [x(x-4)^3] = 3x(x-4)^2 +(x-4)^3`

`d/dx [x(x-4)^3] = (x-4)^2 (3x+x-4)`

`d/dx [x(x-4)^3] = 4(x-4)^2 (x-1)`