Chapter 3.2, Problem 51E

Suppose that $P$, $y$ and $t$ are variables, where $P$ is a function of $y$ an $y$ is a function of $t$.

Write the derivative symbols for the following quantities (i) the rate of change of $y$ with respect to $t$, (ii) the rate of change of $P$ with respect to $y$,(iii) the rate of change of $P$ with respect to $t$. Select your answers from the following:

$\frac{dP}{dy},\frac{dy}{dP},\frac{dy}{dt},\frac{dP}{dt},\frac{dt}{dP},$ and $\frac{dt}{dy}$.

Write the chain rule for $\frac{dP}{dt}$.