Question

Let xy=1

and let dy/dt=5

Find dx/dt when x=5

Answer 1

So the first step is to take the derivative of xy=1. Don't forget the product chain rule!

$xy=1 \\x=5 \\y= \frac{1}{x}=\frac{1}{5} \\ \\\frac{dy}{dt}=5 \\ \\x\frac{dy}{dt}+y\frac{dx}{dt}=0 \\ \\5\times5+ \frac{1}{5} \frac{dx}{dt}=0 \\ \\\frac{1}{5} \frac{dx}{dt}=-25 \\ \\ \frac{dx}{dt}=-125$