Question

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

Answer 1

2(3x^2-1)

Explanation:

`f(x)=2x(x^2-1)`

`df/dx=2(dx/dx.(x^2-1)+xd/dx(x^2-1))`
Product rule:
`d/dx(uv)=(du/dx)v+u(dv/dx)`
`df/dx=2((x^2-1)+x.2x)`

`df/dx=2(x^2-1+2x^2)=2(3x^2-1)`