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

## (a) $f^{\prime}(x)=e^{x}\left(x^{2}+2 x-1\right)$ and $f^{\prime \prime}(x)=e^{x}\left(x^{2}+4 x+1\right)$(b) -14

Derivatives

Differentiation

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### Video Transcript

Yes. Close. So when you married here, so we have ever backs is equal to x square minus one times e to the X. We're gonna find our derivative by using the product rule yet to ex homes, Eat the X goes eat two x times X square minus one. This is equal to eat the X x square plus to minus one. To get our second derivative, we're gonna use the product rule again. Get E to the X from specs square Those two X minus one must two X plus two e to the X, which is equal to eat The axe. Times Square was for X plus one. Next, we're going to draw our graphs wound. Don't look like this.

Derivatives

Differentiation

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