please someone help me with this:
Consider the curve
The equation of the tangent line to the curve at the point has the form where
You are clearly confusing functions of several variables with functions of a single variable. To get the tangent to a curve defined by the relation f(x, y) = c you need to calculate dy/dx. To do this you either make y the subject (where possble or convenient) and differentiate or you just differentiate the relation using implicit differentiation and then solve for dy/dx. Either way, f(x, y) = c defines a function of a single variable.