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Determine the derivative.$$f(x)=\frac{e^{x}+1}{x^{2}-1}$$

$\frac{\left(x^{2}-2 x-1\right) e^{x}-2 x}{\left(x^{2}-1\right)^{2}}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 4

The Derivative of the Exponential Function

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So this problem is going to use the closer rule because you can tell it's a giant quotient. But inside of the question, Will will also have to use the chain rule. Because as you look at the problem, actually, we won't need the general because, well, you'll see when we get to it. We have eat of the X plus one over X square minus one. And, uh, yeah, So if this is named as ffx, we're gonna find the derivative, which, uh, question rule says take the derivative of the top or the derivative of E to the X is E to the X, the derivative of 10 So there's no need to write that you leave X squared minus one alone. Uh, the question rule says minus take the derivative of the bottom Now, which is two X as you leave the top alone. Either the X plus one all over the denominator X squared, minus one squared. Now, as I'm looking at, sometimes teachers will ask you to simplify this. I don't really see a reason to simplify this. Um, this should be a good enough answer. The only thing is, I think you can combine a like term because if you look at you know, if you were to distribute in the numerator, whoops posted their own eat of the X Times X squared minus E to the X minus two X e to the X minus two x. You could combine my terms somewhere in here, but even then I don't know if that would even be worth your while. So I don't think it. I don't think it's advantageous to do that. Eso I would stop with my circled answer. Um, but you could try to simplify if you want.

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