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

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Answer 1 · 2016-05-05T15:07:23

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

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

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