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Find the derivative of each function by using the quotient rule.$$u=\frac{4}{v^{2}}$$

$\frac{d y}{d x}=-\frac{8}{x^{3}}$

Calculus 1 / AB

Chapter 23

The Derivative

Section 6

Derivatives of Products and Quotients of Functions

Derivatives

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as we're looking at this problem, you actually don't need the quotient rule to get the correct answer. So kind of a as a side note, you could actually just know the rule of exponents um that that's equal, so then D. U D V would be equal to negative eight beat the negative third power, which I'll explain anyway. So identify your quotient right there. So when you do the quotient rule, D U D. B. You take the director of the top which is zero and you leave the bottom alone, which is actually just that minus. Now, you leave the top alone. Times the derivative of the bottom, all over the denominator B squared squared. So you probably notice that zero times anything is just zero. So what I'm left with is negative eight B. And when you take a power tool power, you multiply the exponents. So two times two is four and just think about it. It's the same thing as negative eight B. With four B's on bottom. So you could cancel out uh, one of those V's. So the correct answer, as I mentioned earlier is going to be negative eight over B to the third power. So that's your correct derivative. Um And I guess the work on the left is the quotient rule, but you didn't actually need it to get the right answer.

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