Calculus [finding slope of tangent line]
posted by Ali .
Find the slope of the tangent line to the curve 0x^2−2xy+2y^3=10 at point (4,1)
Help please? Thanks in advance

Don't know why you bother with the zero:
−2xy+2y^3=10
(yes, (4,1) is on that graph.
just use the product rule, remembering that x' = 1:
2yx'  2xy' + 6yy' = 0
2y + (6y2x)y' = 0
y' = 2y/(6y2x)
at (4,1),
y' = 2(1)/(6(1)2(4)) = 2/(6+8) = 1/7