step by step for d/dx (x(x-1)^2)

Question

i need help on how to solve the equation above, step by step. Do i use the product rule?

Answer 1

Two ways of doing this:

1. Expand the expression: x(x-1)^2=x^3-2x^2+x, then differentiate: 3x^2-4x+1=(3x-1)(x-1)
2. Use the product rule: let u=x, v=x-1. d(uv)/dx=vdu/dx+udv/dx=(x-1)^2+x(2(x-1))=x^2-2x+1+2x^2-2x=3x^2-4x+1=(3x-1)(x-1).