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Numerade Educator

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Problem 37 Medium Difficulty

(a) If $ f(x) = (x^3 - x)e^x, $ find $ f' (x). $
(b) Check to see that your answer to part (a) is reasonable by comparing the graphs of $ f $ and $ f'. $

Answer

(a) $e^{x}\left(x^{3}+3 x^{2}-x-1\right)$
(b) See explanation for result

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Video Transcript

it's clear. So when you raid here, So we're gonna find the derivative of ex cute minus X times each backs. We're gonna use our product rule to get X cubed minus x the derivative of E to the X plus e to the X times the derivative of X cubed minus x No. When we differentiate it, get X cubed minus X b to the X plus e to the X terms three X square minus one and we got to simplify. Eat the x X cubed plus three X square minus X minus one for part B. We draw a graph and you look like this. You have our normal graph. We'll have our normal graph in black, then are derivative and red.