a particle moves along the curve xy=10. if x=2 and dy/dt=3, what is the value of dx/dt.

Question

i'm guessing this is something to do with parametric equations.

if x is 2, then y=5. but how do i get dx/dt.

you have to differentiate the equation with respect to t
so xy=10
x(dy/dt) + y(dx/dt) = 0

when x=2 y = 5 and dy/dt = 3

so 2(3) + 5(dx/dt) = 0
etc. solve for dx/dt

Answer 1

-6/5