A particle moves along a hyperbola xy = 12. As it reaches the point (4, 3), the y-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant? 9

Question

A particle moves along a hyperbola xy = 12.

 As it reaches the point (4, 3), the y-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?

Answer 1

another approach

is x=12/y

dx/dt=(-12/y²)(dy/dt)

which gives same answer

Answer 2

xy = 12

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

So, dx/dt = -x(dy/dt) / y = -(4cm)(-3cm/sec) / (3cm) = 4 cm/sec

x is increasing at the rate pf 4 cm/sec