Question

For each function u(x) in Exercises 9–12, write the differential du in terms of the differential dx.

$u\left(x\right)=\frac{1}{x}$

Short answer

The differential du in terms of the differential dx is $du=-\frac{1}{x^2}dx$.

Step-by-step solution

Step 1. Given Information

For given function u(x) we have to write the differential du in terms of the differential dx.

$u\left(x\right)=\frac{1}{x}$

Step 2. Now finding the differential du in terms of the differential dx. 

$$\begin{gathered} u\left(x\right)=\frac{1}{x} \\ u\left(x\right)=x^{-1} \\ \frac{du}{dx}=-1x^{-2} \\ \frac{du}{dx}=-\frac{1}{x^2} \\ du=-\frac{1}{x^2}dx \end{gathered}$$