How do you find dy/dx?

cnyce05

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
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
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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