U(x,y)=4x^2 + 3y^2... Calculate dy/dx for dU=0, that is, what is the implied trade off between x and y holding U constant? The answer is dy/dx=-4x/3y... Why? How?

Question

anonymous · Answer

I learned this recently in Precalc but dont remember... Look here for help http://www.mathsisfun.com/calculus/derivatives-dy-dx.html

anonymous · Answer

This is multivariate calculus

anonymous · Answer

$$dU = 8xdx + 6ydy = 0$$
So..
$$\frac{ dy }{ dx } = \frac{ -8x }{ 6y }$$

anonymous · Answer

See? And that obviously reduces to 
-4x/3y

anonymous · Answer

oh wow, yea i get it! sweet! thanks!

anonymous · Answer

np!

anonymous · Answer

real quick, why is 8x negative?

anonymous · Answer

Hang on.

anonymous · Answer

$$8xdx+6ydy=0$$
$$6ydy=-8xdx$$
Divide 6y from the left side and dx from the right side.

anonymous · Answer

I have to get the hang of all this math. I studied economic policy in undergrad and all this math in graduate level economics is getting to me, but I'm taking notes.

anonymous · Answer

oh, ok

anonymous · Answer

I'm not familiar with economics, but you'll get the hang of it real quick definitely.

anonymous · Answer

Well, these types of problems. idk what other types you have haha.

anonymous · Answer

I can talk about economics all day.