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Okay, let's look at this problem, associate is
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a long resume function. The first step we want
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to do is to use that differential rule of natural
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log function. So we got h its prime X
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equals two. One over X plus square root.
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Oh X squared minus one. Okay, we treat
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this as a whole and then we have to differentiate
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this thing. Then we got X plus square root
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X squared minus one crime. Right? How do
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we deal with saying? Well, we have to
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use the sum rule and chain rule as well as
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the power route to solve this. And for before
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that I want to rewrite this as a power for
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. So we have one over X plus Beirut X
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squared minus one times X plus on half mm I'm
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plus square minus one. It was a one half
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power and then prime. Okay then copy this down
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here. X square plus square square root tech square
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minus one climbs. Okay, so the dream team
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of actually just one right And the duty of of
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this thing. We use the power route we got
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x squared minus one times. Okay, Just took
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one minus one half in just 91 half. Right
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, okay. Then we have to use the chain
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group because this is another single variable. It's a
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expressive expression. Right? So we have to you
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will find the derivative of X squared minus one.
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Just the two X. Okay then coming this down
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here. What over X plus square root square minus
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one times. Okay, for this whole thing,
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the negative, what has of X square minus one
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is just one over square root X squared minus one
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. Right? Then we can write this as square
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root of square minus one. The numerator, it's
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one times two X. It's just two X.
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Okay? Yeah, then we can write down yes
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one over X plus square root X squared minus one
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. And we rewrite this as Okay? So first
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we can we see this to to we can cancel
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all the tooth and we write this as x squared
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minus one over x squared minus one. Right?
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That just you close to one, right? And
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we plus X over square minus one. Okay,
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so here we got copy this down. As usual
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. We got X square minus one square root of
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X squared minus one plus X over x squared minus
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one square root of x squared minus one. Right
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. And we noticed that this thing on the numerous
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not the denominator and this thing on the numerator,
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they're actually the same. Right? So we can
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cancel out these two items. And finally all the
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things left is just one over square root of X
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. Square one. Is what? Okay, that's
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a solution of this problem. Thank you.