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Numerade Educator

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Problem 27 Medium Difficulty

Find $ f'(x) $ and $ f"(x). $

$ f(x) = (x^3 + 1)e^e $

Answer

$=e^{x}\left(x^{3}+6 x^{2}+6 x+1\right)$

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Video Transcript

it's Claire's, the one you right here. So we're given up of X is equal to x cubed plus one turns e to the X We're gonna differentiate by applying the product rule and we get X cubed plus one d over t x Eat the X plus b to the x d over d x X cute plus one and we're gonna apply to some rule And when we simplify, we get e to the X times X cubed plus three X square close one. Now we're gonna determine second derivative So we're just gonna take the derivative of the 1st 1 We're just gonna ply the product and some rule once again and we get X cubed plus three x square plus one D over d x her e to the X plus e to the x d over d X execute plus three X square plus one. This becomes equal to X cubed less three x square plus one comes Eat the x close Eat the x three X square plus six sex because is equal to X cubed plus six x square plus six x plus one tongues heat, fax