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Determine the derivative.$$f(x)=e^{x}(x-1)$$

$x e^{x}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 4

The Derivative of the Exponential Function

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Determine the derivative.<…

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Calculate the derivative.<…

Okay. Our task is to find the derivative of this function that has e to the X Times X minus one. And there are a couple of ways of doing this problem May. I'll show you both because neither will take very long. The first way, the way I would do is identify that you have a product in here. Eso you want to do the product rule? What is the product rule? Would be, uh, the derivative of the left side, which is e to the X. You leave the right side alone, explained sworn. But then you have to subtract off. Sorry, Ad product rolls ad. Uh, you leave the left side alone, which looks the same because the director of the feet of the X is itself a multiply by the derivative of the right side, which is one. But now it would actually make sense to distribute this either the into the problem. So looking at X E to the X minus either the X Times one beat either the X and then plus E to the X. You can actually see these two pieces will cancel. So your answer for the derivative is simply X e to the X, which would make sense if you were to do this problem slightly different and distribute that in. You have X E to the X uh, minus e to the X. And if you did the derivative that way, you still have a product for which is why I wouldn't do the problem this way. Well, the derivative of the left side of the one they need the X plus leave exit derivative of either the X and then the directive PDD X. You still get pieces to cancel and you get the same answer so your choice but answers X e to the X.

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