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Numerade Educator

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Problem 38 Medium Difficulty

(a) If $ f(x) = e^x/ (2x^2 + x + 1), $ find $ f' (x). $
(b) Check to see that your answers to part (a) are reasonable by comparing the graphs of $ f, f', $ and $ f". $

Answer

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

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Video Transcript

it's clear. So when you raid here, So we're gonna take the derivative and we're gonna apply our quotient role. And we got two x square plus x plus one times e to the X minus. Each of the ex comes for X plus one all over X square, two X square plus X plus one square. This becomes equal to sex each X Times two X minus three All over to X square plus X plus one square For a second part, we're gonna draw a graph. I'll draw our original in black so look like this and then our derivative and red