Let xy = 5 and { dy }/{ dt } = 3.

Question

Find { dx }/{ dt } when x = 1.

Answer 1

xy = 5 , use the product rule and differentiate with respect to t
x(dy/dt) + y(dx/dt) = 0

when x= 1 ---> (1)y = 5, so y=5
now sub in all that stuff in
x(dy/dt) + y(dx/dt) = 0
(1)(dy/dt) + 5(3) = 0
dy/dt = -15