Related Rates: Suppose that a point is moving along the path xy=3 so that dy/dt=2. Find dx/dt when x=5

Question

I'm just having a tough time understanding how to do the problem entirely, so being as specific as possible would be extremely helpful. :)

Answer 1

$xy = 3$

or, $\frac{dx}{dt}y + x\frac{dy}{dt} = 0$ (Derivative of a constant wrt $t$ is 0) .................................... (1)

Since $xy = 3$ and

$x = 5$ (Given) .................................... (2)

Therefore $y = \frac{3}{5}$ .................................... (3)

$\frac{dy}{dt} = 2$ (Given) .................................... (4)

Now use (2), (3), (4) in (1) to calculate $\frac{dx}{dt}$

Finally $\frac{dx}{dt} = -\frac{50}{3}$