Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3: 17

Answer

$y' = 3x^2e^x+x^3e^x$

Work Step by Step

In order to derivate this function you have to apply the product rule $\dfrac{d}{dx}(ab) = a'b+ab'$ Then let's identify a and b and derivate them $a=x^3$ $a' = 3x^2$ $ b=e^x$ $ b'=e^x$ Then substiute in the formula, simplify and get the answer: $y' = 3x^2e^x+x^3e^x$
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