(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to prove that if [tex] y = \frac{u}{v} [/tex]

then [tex] \frac{dy}{dx} = \frac{ v \frac{du}{dx} - u \frac{dv}{dx} }{v²} [/tex]

u and v are functions of x.

2. The attempt at a solution

[tex] y = uv^{-1} [/tex]

[tex] y + dy = ( u + du ) ( v + dv )^{-1} [/tex]

then I suppose I could use Newton's Binomial to develop

[tex] ( v + dv )^{-1} [/tex]

but I don't know how to use the formula

[tex] (a+b)^{n} = \sum_{k=0}^{n} \dbinom{n}{k} a^{n-k} b^k [/tex]

with a negative exponent. I'm familiar with binomial coefficients but that negative exponent is leaving me without a clue.

Any help would be very much appreciated, thank you!

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# Homework Help: Need help with quotient rule

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