Find dw/dt for w = xy + z if x = cos t, y sin t, and z = t. Find ∂w/∂r when r = 8 and s = – 8 if w = (x + y + z) ² , x = r – s, y = cos (r+s), and z = sin (r + s).

Assuming that 2x ³ + 6y ² – 3xy = 0 defines y as a differentiable function of x, use the theorem dy/dx = F F _x /F _y to find dy/dx at (1, 1).