How do you differentiate f(x)=(-e^x+x)(3x^3-x) using the product rule?

1 Answer
May 24, 2016

See below.

Explanation:

By the product rule d/dxu(x)v(x)=u'(x)v(x)+v'(x)u(x)
Therefore, if we let u(x)=-e^x+x and v(x)=3x^3-x
Then d/dx(-e^x+x)(3x^3-x)=(-e^x+x)'(3x^3-x)+(3x^3-x)'(-e^x+x)
(-e^x+x)'=-e^x+1
(3x^3-x)'=9x^2-1
Therefore, the derivative =(-e^x+1)(3x^3-x)+(9x^2-1)(-e^x+x)
You could then expand and simply to finish off.