Use implicit differentiation to find the slope of the tangent line to the curve x^{2}+xy-2y^{3}=4 at the point (2,1).

Question

Use implicit differentiation to find the slope of the tangent line to the curve x^{2}+xy-2y^{3}=4​ at the point (2,1)​.

Mark M. · Accepted Answer

x2 + xy - 2y3 = 42x + x(dy/dx) + y - 6y2(dy/dx) = 0dy/dx(x - 6y2) = -2x - ydy/dx = (-2x - y) / (x - 6y2)Evaluate when x = 2 and y = 1.

1 Expert Answer