How do you differentiate #y=(1+x^2)e^x #?

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Answer 1 · 2016-05-19T16:16:28

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

#(1+x^2)e^x#

This is of the form:
#f(x)=g(x)h(x)#

Where,
#g(x)=1+x^2# and #h(x)=e^x#

Apply the product rule to find the derivatives:
#f(x)=g(x)h(x)#

#=>f'(x)=g'(x)h(x)+g(x)h'(x)#

Let's work out the derivatives of the functions, separately:

#g(x)=1+x^2#

#g'(x)=2x#

#h(x)=e^x#

#h'(x)=e^x#

Plug in these values in #f'(x)#

#f'(x)=g'(x)h(x)+g(x)h'(x)#

#=2x xx e^x+(1+x^2)xxe^x#

#=2xe^x+e^x(1+x^2)#