Question

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

Answer 1

`d/dxx(x^2-2x+1)^4=(8x^2-8x)(x^2-2x+1)^3+(x^2-2x+1)^4`

Explanation:

According to the product rule,
`d/dx [f(x)*g(x)]=f(x)*g'(x)+g(x)*f'(x)`

`therefored/dxx(x^2-2x+1)^4=(x)*4(x^2-2x+1)^3(2x-2)+(x^2-2x+1)^4`