1. ## Implicit Differentiation

Hi, I need some help with ^. I kind of feel embarrassed asking this question because it seems so easy. (I'm not sure if this belongs in Calc or PreCalc. I'm in PreCalc, but differentiation is Calc right?)

The problem is $\displaystyle x^3+y^3=125$

I want to find dy/dx, and the answer choices are

a. [tex]-x/y[/Math]
b. $\displaystyle -x/5y$
c. $\displaystyle y/x$
d. $\displaystyle x/(y-5)$
e. $\displaystyle x/y$

Well, my reasoning is that it should be $\displaystyle -(x/y)^2$, but it's not on the answer choices. It should also be negative and be devoid of the 5's right? Well, when left with -x/y ($\displaystyle dy/dx of x^2+y^2=C$)

Am I approaching the problem wrong or am I misunderstanding implicit differentiation.

2. Originally Posted by FragKrag
Hi, I need some help with ^. I kind of feel embarrassed asking this question because it seems so easy. (I'm not sure if this belongs in Calc or PreCalc. I'm in PreCalc, but differentiation is Calc right?)

The problem is $\displaystyle x^3+y^3=125$

I want to find dy/dx, and the answer choices are

a. $\displaystyle -x/y$
b. $\displaystyle -x/5y$
c. $\displaystyle y/x$
d. $\displaystyle x/(y-5)$
e. $\displaystyle x/y$

Well, my reasoning is that it should be $\displaystyle -(x/y)^2$, but it's not on the answer choices. It should also be negative and be devoid of the 5's right? Well, when left with -x/y ($\displaystyle dy/dx of x^2+y^2=C$)

Am I approaching the problem wrong or am I misunderstanding implicit differentiation.
Yes, it would be $\displaystyle -\left(\frac{x}{y}\right)^2$

The answer would have been (a) if the question was to implicitly differentiate $\displaystyle x^{{\color{red}2}}+y^{{\color{red}2}}=125$...

--Chris