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= (1)/(x)=(1)/(5) \\ \\(dy)/(dt)=5 \\ \\x(dy)/(dt)+y(dx)/(dt)=0 \\ \\5*5+ (1)/(5) (dx)/(dt)=0 \\ \\(1)/(5) (dx)/(dt)=-25 \\ \\ (dx)/(dt)=-125`