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

1 Answer
Apr 7, 2016

Answer:

#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)#