Assume x and y are functions of t Evaluate dydt for 3xy 5x2y

Assume x and y are functions of t. Evaluate dy/dt for 3xy -5x+2y^3 = -82 With the conditions dx/dt= -6, x=2, y=-3

3xy -5x +2y^3 = -82

differentiate w.r.t t

3xdydt +3ydx/dt -5dx/dt + 2*3y^2dy/dt = 0

Given : dx/dt = -6, x=2, y=-3

3*2dy/dt + 3*(-3)(-6) - 5*(-6) + 6(-3)^2dy/dt =0

6dy/dt + 54 + 30 + 54dy/dt =0

60dy/dt + 84 =0

dy/dt = -84/60

dy/dt = -7/5