What is the slope of the tangent line of #x^3-(xy)/(x-y)= C #, where C is an arbitrary constant, at #(1,4)#?
The slope is
So the curve we are being asked about has equation:
Simplifying gets us the equation:
Note that this equation is linear in
(If you're serious about learning mathematics, try solving for
Differentiating implicitly gets us:
Rather than solving algebraically first, I think it is simpler to substitute the values now.
(Again, trying the other order --solving for
Do the artihmetic/algebra to get