Chapter 6.4, Problem 10QR

To determine

To find: The derivative of the given function.

Answer to Problem 10QR

The derivative is given by $\frac{1}{3x}$

Explanation of Solution

Given Information:

The function $\frac{dx}{dy}=3x$

Formula used:

Here, the function given is $\frac{dx}{dy}$ . The relation between $\frac{dy}{dx}$ and $\frac{dx}{dy}$ when both functions are defined is,

  $\frac{dy}{dx}=\frac{1}{\raisebox{1ex}{$dx$}\!\left/ \!\raisebox{-1ex}{$dy$}\right.}$

Calculation:

Given the function $\frac{dx}{dy}=3x$

Using the relation in (1), the derivative,

  $\begin{array}{c}\frac{dy}{dx}=\frac{1}{\raisebox{1ex}{$dx$}\!\left/ \!\raisebox{-1ex}{$dy$}\right.}\\ =\frac{1}{3x}\end{array}$