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How do you differentiate #f(x)=(4e^x+1)(x^2-3)# using the product rule?

1 Answer

Jun 5, 2018

#f'(x) = 4e^x(x^2+2x-13) + 2x#

Explanation:

#f(x) = (4e^x+1)(x^2-3)#

Click here for details on the product rule.
#f'(x) = d/dx(4e^x + 1)(x^2-3) + (4e^x + 1)d/dx(x^2-3)#

#f'(x) = (4e^x)(x^2-3) + (4e^x + 1)(2x)#

To simplify, we'll expand and see if we can condense it later:
#f'(x) = 4 e^x x^2 - 12e^x + 8 x e^x + 2x#

#f'(x) = 4e^x(x^2+2x-13) + 2x#

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