find dy/dt and dx/dt

Question

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

xy = 6

(a) Find dy/dt, given x = 6 and dx/dt = 15.

dy/dt =

(b) Find dx/dt, given x = 1 and dy/dt = –6.

dx/dt =

Answer 1

Differentiate: D_t(xy) = x (dy/dt) + y(dx/dt)...now plug in the values given.