How to show that $\frac{dy}{dx}=\frac{dy}{d(x-c)}$? It seems intuitive to me that $\frac{dy}{dx}=\frac{dy}{d(x-c)}$ (the derivative of $y$ with respect to $(x-c)$, where $c$ is a constant), since subtracting a constant from $x$ doesn't change the slope of $y$, but how can I show it? Thanks in advance.

Note that if $z=x-c$ then the chain rules says that
$$\frac{dy}{dz} = \frac{dy}{dx}\cdot \frac{dx}{dz} = \frac{\frac{dy}{dx}}{dz/dx}=\frac{dy}{dx}.$$
