Question

In the problem, x and y are differentiable functions of t. Find dx/dt when x = 9, y = 2, and dy/dt= 2.

x^3y^2 = 2916

Answer 1

f(x,y) = x^3y^2
df = (df/dx) dx + (df/dy) dy

df/dt=(df/dx) dx/dt + (df/dy) dy/dt
but f is a constant = 2916

df/dx = 3x^2y^2 = 3*81*4= 972
df/dy = 2x^3y = 2*729*2= 2916

so 0 = 972 (dx/dt) + 2916 (2)
dx/dt = -6