Proving for $u=f(x,y), v=g(x,y)$, $\frac{du}{dx}\frac{dx}{du}+\frac{dv}{dx}\frac{dx}{dv}=1$.

Question

How do you prove:

If u and v are differentiable, $$u=f(x,y), v=g(x,y)$$ Prove

$$\frac{\partial u}{\partial x}\frac{\partial x}{\partial u}+\frac{\partial v}{\partial x}\frac{\partial x}{\partial v}=1$$

I have no idea how to start. Do we have to use the Jacobian determinant?