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Find $f^{\prime}(x), f^{\prime \prime}(x),$ and $f^{\prime \prime \prime}(x)$$$f(x)=\frac{x}{x+2}$$

$f^{\prime \prime \prime}(x)=6(x+2)^{-3}+-6 x(x+2)^{-4}$

Calculus 1 / AB

Chapter 3

Derivatives

Section 3

The Product and Quotient Rules

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

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Okay, so let's rewrites or quotient products sort of exercise exports to probably have one. And I was take a derivative. So we get to vote over facts. That's one times, like supposed to through a park later. One plus x times derivative of this term. That's the negative exposed to the power of native to okay. And now let's take our second derivative. That's equal to derivative of this term. That's negative. One exposed to to have new to plus we use our product will hear sort of a X that's just one. So that's thinking of the next closed due to our negative, too. And we have plus the derivative list. ERM, that's negative, too. And then we're changing negative excellent triples X and then exposed to the power of three threat people to native to exports to our neighbor to and in plus two X experts to part of the debris. And I'm taking or through a derivative, we use our product there. Okay, that's not before exposed to the power of negative three, plus a good group of ex That's 1 to 2 x close to who have they got? Three. So you find that to be six of what we have here and in time to develop Liston. And then we have times two x so that's moving down and three. So that's like three times, too. It's not your six x and extras to Power of Nick before. Okay, so we get our three year evidence here.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

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