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**1. Homework Statement**

Use implicit differentiation to show that the one parameter family f(x, y)=c satisfies the differential equation dy/dx = [tex]-f_{x}/f_{y} [/tex], where [tex]f_{x}=\frac{\partial f}{\partial x} [/tex] and [tex]f_{y}=\frac{\partial f}{\partial y} [/tex].

**2. Homework Equations**

**3. The Attempt at a Solution**

Well, my teacher said I need to use the chain rule, but I'm confused about how to differentiate something that is in the general form f(x, y). And if f(x, y)=c, doesn't the derivative trivially equal 0?

Thanks in advance for the help.