Question

Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .

Answer 1

Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9