What is the slope of the tangent line of # (xy-1/(yx))(xy+1/(xy)) =C #, where C is an arbitrary constant, at #(1,5)#?
We are told that the point
So we can find
As written, this looks tedious to differentiate implicitly, so let's rewrite it as:
Or better, still,
Solving for the derivative gets us
Regardless of the constant, at