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

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Answer 1 · 2015-12-03T02:15:34

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

According to the Product Rule:

#f'(x)=(2+x^(-2))d/dx[e^x]+e^xd/dx[2+x^(-2)]#

Find each derivative separately.

#d/dx[e^x]=e^x#

#d/dx[2+x^(-2)]=-2x^(-3)#

Plug back in.

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

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