assume that x and y are both differentiable function of t.

Question

find dx/dt when x = 11 and dy/dt =-8 for xy=55

Answer 1

xy = 55

when x = 11

11y = 55

y = 55/11

y = 5

xy =  55

Take d/dt of both sides and differentiate implicitly.

Apply product rule d/dx[uv] = uv' + vu'.

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

y(dx/dt) = - x(dy/dt)

dx/dt = - (x/y)(dy/dt)

Substitute x = 11, y = 5 and dy/dt = - 8 in above equation.

dx/dt = - (11/5)(-8)

dx/dt = 88/5.