Find dy/dt. Let for 4xy-7x+4y^3=-92 and dx/dt=-16 when x=4, y=-2

Question

Find dy/dt. Let for 4xy-7x+4y^3=-92 and dx/dt=-16 when x=4, y=-2

Answer 1

4xy-7x-4y³=-92

Using implicit differentiation

4y dx/dt+4x dy/dt -7 dx/dt + 12y²dy/dt = 0

(4x+12y²)dy/dt + (4y-7) dx/dt = 0

dy/dt = (7-4y)/(4x+12y²) dx/dt

when x=4, y = -2 and dx/dt = -16

dy/dt = (15/64) (-16) = -15/4