Related rates

Recall how we define inverses: $$\begin{alignat}{2} &\text{implicit} & &\text{explicit} \\ x & = \sin y &\to y&= \sin^{-1}x \\ x &= e^{y} & \to y &= \ln x \end{alignat} $$ So these are just solutions of equations, but the relation between $x$ and $y$ os present in both. Except, it's implicit in the first column.