`f(x) = (x^3 + 2x)e^x` Differentiate.

Expert Answers
growley52 eNotes educator| Certified Educator

`f(x) = [g(x)][h(x)]`

`f'(x) = g'(x)[h(x)] + g(x)[h'(x)]`

`g(x) = x^3 + 2x, g'(x) = 3x^2 + 2`

`h(x) = e^x, h'(x) = e^x`

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  So, `f'(x) = (3x^2 + 2)e^x + (x^3 + 2x)e^x`

`=(3x^2)e^x + 2e^x + (x^3)e^x + 2xe^x`

`=(x^3 + 3x^2 + 2x + 2)e^x`

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balajia | Student

`f'(x)=(3x^2+2)e^x+(x^3+2x)e^x`

`=(x^3+3x^2+2x+2)e^x`

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