Please Help with this

Question

Let xy=2 and dy/dt=4.

Find dx/dt when x=5.

Answer 1

xy = 2

find dy/dt= 4, find dx/dt when x= 5 and y = 2/5

xy' + yx' = 0

x' = -xy'/y = -5(4)/(2/5)= -20)(5/2) = -50 = dx/dt

Answer 2

Since x = 5 and xy = 2, y = 2/x = 2/5

x(dy/dt) + y(dx/dt) = 0

Since dy/dt = 4, we have (5)(4) + (2/5)(dx/dt) = 0

Solve for dx/dt.