1. Quotient rule for derivatives

I am trying to use the quotient rule on this:

$\displaystyle % MathType!MTEF!2!1!+- % faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaWaaSaaaeaadaGcaaqaaiaadIhaaS qaba % aakeaadaGcaaqaaiaadMhaaSqabaaaaaaa!305D! $\frac{{\sqrt x }}{{\sqrt y }}$$

I was taught the quotient rule as:

$\displaystyle % MathType!MTEF!2!1!+- % faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaWaaSaaaeaacaWGMbGaai4jaiaadE gacq % GHsislcaWGMbGaam4zaiaacEcaaeaacaWGNbWaaWbaaSqabeaa caaI % Yaaaaaaaaaa!35E8! $\frac{{f'g - fg'}}{{g^2 }}$$ which has been working fine until I hit this question while studying at home.

I don't know whether to take the derivative of the denominator as the derivative of $\displaystyle % MathType!MTEF!2!1!+- % faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaGaamyEamaaCaaaleqabaGaaGymai aac+ % cacaaIYaaaaaaa!3167! $y^{1/2}$$ or the derivative of $\displaystyle % MathType!MTEF!2!1!+- % faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaGaamyEamaaCaaaleqabaGaeyOeI0 IaaG % ymaiaac+cacaaIYaaaaaaa!3254! $y^{ - 1/2}$$ because it is in the denominator? I'm confused because I can rewrite the function as $\displaystyle % MathType!MTEF!2!1!+- % faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj % 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x % bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq % pepae9pg0FirpepeKkFr0xfr-xfr-xb9Gqpi0dc9adbaqaaeGaciGa % aiaabeqaamaabaabaaGcbaGaamiEamaaCaaaleqabaGaaGymai aac+ % cacaaIYaaaaOGaamyEamaaCaaaleqabaGaeyOeI0IaaGymaiaa c+ca % caaIYaaaaaaa!35B2! $x^{1/2} y^{ - 1/2}$$. What is my g for this formula? Thanks in advance, gurus!!!

2. Treat it as $\displaystyle \displaystyle y^{\frac{1}{2}}$.