How to calculate $\frac{d}{d y} y'$

Question

Is there a way to evaluate the following expression?

$$ \frac{d}{dy} y' $$

where

$$ y' = \frac{dy}{dx}.$$

Answer 1

By the Chain Rule,

$$\begin{align}\frac{dy'}{dy} &= \frac{dy'}{dx}\cdot\frac{dx}{dy}\\ &= y'' \cdot \frac{1}{y'}\\ &= \frac{y''}{y'}\end{align}$$