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

1 Answer
Apr 7, 2016

f'(x)=xe^(x^2-x)(2x^2-x+2)

Explanation:

f(x)=x^2e^(x^2-x)

Differentiating both sides w.r.t 'x'

f'(x)=d/(dx)(x^2e^(x^2-x))

Taking x^2 as first function and e^(x^2-x) as second function

f'(x)=x^2d/(dx)(e^(x^2-x))+e^(x^2-x)d/(dx)(x^2)

f'(x)=x^2(e^(x^2-x))d/(dx)(x^2-x)+e^(x^2-x)(2x)

f'(x)=x^2(e^(x^2-x))(d/(dx)(x^2)d/(dx)(-x))+e^(x^2-x)(2x)

f'(x)=x^2(e^(x^2-x))(2x-1)+2xe^(x^2-x)

f'(x)=2x^3e^(x^2-x)-x^2e^(x^2-x)+2xe^(x^2-x)

f'(x)=e^(x^2-x)(2x^3-x^2+2x)

f'(x)=xe^(x^2-x)(2x^2-x+2)