💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!



Numerade Educator



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'. $


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

More Answers


You must be signed in to discuss.

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.