How do you differentiate #f(x)=(e^x+x)(x^2-3)# using the product rule?

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Answer 1 · 2018-03-17T16:35:34

#f^(')(x) =(e^x+1)(x^2-3) + (e^x+x)(2x)#

or

#f^(')(x)=(x^2+2x-3)e^x +3(x^2-1)#

Start:

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

#f^(')(x) =(e^x+1)(x^2-3) + (e^x+x)(2x)#

Rearrange if you wish:

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

# = (x^2+2x-3)e^x +3(x^2-1)#