If 3x^3+x^2y-xy^3=-1, then the slope of the curve at point (1,0) is?

Question

I've been stuck on this problem for hours

Answer 1

You need to find dy/dx by differentiating the equation as follows

9x² +x²(dy/dx) +2xy-2xy²(dy/dx)-y³=0

Collect terms(x² -2xy²)(dy/dx) = y³-2xy-9x²

Now plug in the values for x and y and you will have your answer!

P.S. Remember as you differentiate that you must use the product rule for derivatives.