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

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Answer 1 · 2015-12-12T14:28:34

#f'(x)=e^x(x+2)(x+4)#

According to the product rule:

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

Find each derivative.

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

The following differentiation will use the chain rule:

#d/dx[(x+2)^2]=2(x+2)d/dx[x+2]=2(x+2)=2x+4#

Plug these back in.

#f'(x)=e^x(x+2)^2+e^x(2x+4)#

#f'(x)=e^x(x^2+4x+4+2x+4)#

#f'(x)=e^x(x^2+6x+8)#

#f'(x)=e^x(x+2)(x+4)#