How do you find dy/dx?

May 2010
3
0
I do not know how to find the answer to:
dy/dx for x^2 y^2-xy = 2
 

Chris L T521

MHF Hall of Fame
May 2008
2,844
2,046
Chicago, IL
I do not know how to find the answer to:
dy/dx for x^2 y^2-xy = 2
Do you know how to differentiation functions implicitly?

Observe that \(\displaystyle \frac{\,d}{\,dx}\left[xy\right]=x\frac{\,d}{\,dx}\left[y\right]+y\frac{\,d}{\,dx}\left[x\right]=x\frac{\,dy}{\,dx}+y\).

Can you apply this idea when differentiating \(\displaystyle x^2y^2\)?

Once you do that, combine the two results and solve for \(\displaystyle \frac{\,dy}{\,dx}\), as if it was a variable.

Can you take it from here?
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
I do not know how to find the answer to:
dy/dx for x^2 y^2-xy = 2
\(\displaystyle \frac{dy}{dx}=-\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}\)

\(\displaystyle =\frac{y-2xy^2}{2x^2y-x}\)
 
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