Finding derivatives by solving for y' Here's the hyperlink for the picture:  where the differentiation happens, can someone explain why... $$(\ln|y|)' = \frac{1}{y} \cdot y'$$

This is simply the chain rule. It might be more clear what's happening when you write it in Leibniz notation: $$\frac{d}{dx} (\ln|y|) = \frac{dy}{dx} \cdot \frac{d}{dy} (\ln|y|) $$ $$ \Rightarrow \frac{d}{dx} (\ln|y|) = \frac{dy}{dx} \cdot \frac{1}{y}$$ Which in prime notation is just $(\ln|y|)' = (1/y) \cdot y'$.

Definitely would recommend brushing up on the chain rule here: <