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

Textbook Question

Chapter 3, 3.2 - Problem 3 - Calculus: Early Transcendentals (7th Edition, James Stewart).
See all solutions for this textbook.

2 Answers | Add Yours

growley52's profile pic

growley52 | College Teacher | (Level 1) Adjunct Educator

Posted on

`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`

` `

  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`

` `

We’ve answered 318,957 questions. We can answer yours, too.

Ask a question