CALCULUS!!!! help me pleaseeeeeeeeeeeeeeeeeeeeee?

Question

An object is moving along the curve xy=1. The rate of change of y with respect to t is dy/dt=5.
Use implicit differentiation to find dx/dt, when x=1.

Answer 1

xy=1
on differentiating with respect to 't' we get
y(dx/dt)+x(dy/dt)=0

as xy=1 we get y=1/x
and it is given that dy/dt=5

therefore we get
(1/x)(dx/dt)+x(5)=0

dx/dt=-5(x)(x)

at x=1 we get

dx/dt=-5

thats it........

Answer 2

(d/dt).(xy) = 1
y.(dx/dt) + x.(dy/dt) = 0
y . (dx/dt) + 5.x = 0
dx/dt + 5.(x/y) = 0
dx/dt = - 5(x/y) = - 5(x/1/x) = - 5x²
dx/dt = - 5 when x = 1

Answer 3

this is the second F****** math problem this morning i don't know