Question

How do you differentiate `y = (2x^2 + x)(x − x^2)`?

Answer 1

`dy/dx=-8x^3+3x^2+2x`

Explanation:

Product rule states `d/dxf(x)*g(x)=f(x)*dg(x)/dx+df(x)/dx*g(x)`

Differentiating `y=(2x^2+x)(x-x^2)` using product rule

`dy/dx=(4x+1)(x-x^2)+(2x^2+x)(1-2x)`

or `dy/dx=4x^2-4x^3+x-x^2+2x^2+x-4x^3-2x^2`

or `dy/dx=-8x^3+3x^2+2x`