# Thread: Quotient rule for derivatives

1. ## Quotient rule for derivatives

I am trying to use the quotient rule on this:

$% MathType!MTEF!2!1!+-
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq
$\frac{{\sqrt x }}{{\sqrt y }}$
$

I was taught the quotient rule as:

$% MathType!MTEF!2!1!+-
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq
% 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 $% MathType!MTEF!2!1!+-
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq
% aiaabeqaamaabaabaaGcbaGaamyEamaaCaaaleqabaGaaGymai aac+
% cacaaIYaaaaaaa!3167!
$y^{1/2}$
$
or the derivative of $% MathType!MTEF!2!1!+-
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq
% aiaabeqaamaabaabaaGcbaGaamyEamaaCaaaleqabaGaeyOeI0 IaaG
% ymaiaac+cacaaIYaaaaaaa!3254!
$y^{ - 1/2}$
$
because it is in the denominator? I'm confused because I can rewrite the function as $% MathType!MTEF!2!1!+-
% faaagaart1ev2aaaKnaaaaWenf2ys9wBH5garuavP1wzZbqedm vETj
% 2BSbqefm0B1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpe pC0x
% bbL8FesqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaq
$x^{1/2} y^{ - 1/2}$
2. Treat it as $\displaystyle y^{\frac{1}{2}}$.