Brief Calculus.

Question

If 2y + 3x²= -10x find dy/dt at x = 6. If dx/dt = 4.

Answer 1

2 dy/dt + 6x dx/dt = -10 dx/dt (differentiate with respect to t -- since x and y are functions of t, multiply by derivative of the "inside" -- chain rule)

2 dy/dt + 6(6) (4) = -10(4) (substitute given values)

2 dy/dt + 144 = -40

2 dy/dt = -184

dy/dt = -184/2 = -92