Let y = f (x, t), and T = t (x, y) be determined by F (x, y, t) = 0 f. F are differentiable functions

Let y = f (x, t), and T = t (x, y) be determined by F (x, y, t) = 0 f. F are differentiable functions


dy/dx= ∂f/ ∂x + (∂f/ ∂t)(∂t/∂x)
dF/dx= (∂F/∂t)(∂t/ ∂x)+ (∂F/∂y)(∂y/ ∂x) + (∂F/∂x)=0
dy/dx= ∂f/∂x +(∂f/∂t)[dF/dx-(∂F/∂y)(∂y/∂x)-(∂F/∂x)]/(∂F/∂t)