Assume x and y are functions of t. Evaluate dy/dt for 2xy-2x+6y^3=-30, with the conditions dx/dt=-18, x=6, y=-1
Given the equation 2xy - 2x + 6y^3 = -30, we take the derivative of both sides with respect to t:
d/dt (2xy - 2x + 6y^3) = d/dt (-30)
2(d(xy)/dt) + 2x(dy/dt) - 2(dx/dt) + 18(dy/dt)*y^2 = 0
2(x(dy/dt) + y(dx/dt)) - 2(dx/dt) + 18(dy/dt)*y^2 = 0
2(6(dy/dt) + (-1)(-18)) - 2(-18) + 18(dy/dt)*(-1)^2 = 0
12(dy/dt) + 36) + 36 + 18(dy/dt) = 0
12(dy/dt) + 18(dy/dt) = -72
30(dy/dt) = -72
dy/dt = -72 / 30
dy/dt = -2.4