Chapter 3.2, Problem 52E

Suppose that $Q$, $x$ and $y$ are variables, where $Q$ is a function of $x$ and $x$ is a function of $y$. (Read this carefully.)

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

$\frac{dy}{dx},\frac{dx}{dy},\frac{dQ}{dx},\frac{dx}{dQ},\frac{dQ}{dy},$ and $\frac{dy}{dQ}$.

Write the chain rule for $\frac{dQ}{dy}$.