Question

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

xy=6

a) Find dy/dt, given x=8 and dx/dt=12

b) Find dx/dt, given x=1 and dy/dt=-8


I started with a and got dy/dt=dx/dt(-y/x)

Plugging with the given values leaves me with dy/dt=12(-y/8)

There's a y that is not given, how would I find out y in this case???

Answer 1

Finally figured out, simply plug the given x value into the original equation!

Answer 2

This leaves with

dy/dt=12(-.75/8)

dy/dt=-1.125

dy/dt=-9/8

Answer 3

a) y = 6 x^-1
... dy/dt = -6 x^-2 dx/dt
... dy/dt = (-6 / 64) * 12

b) missing y a typo?