Chapter 3.9, Problem 25E

(a)

To determine

To find: The differential of the given function.

Answer to Problem 25E

The differential of the given function is $\frac{e^{x/10}}{10}dx$ .

Explanation of Solution

Given information:

The given function is,

  $y=e^{x/10}$

The differential of the given functionis calculated as,

  $\begin{array}{l}y=e^{x/10}\\ \frac{dy}{dx}=e^{x/10}\left(\frac{d}{dx}\left(\frac{x}{10}\right)\right)\\ \frac{dy}{dx}=\frac{1}{10}{e}^{x/10}\\ dy=\frac{e^{x/10}}{10}dx\end{array}$

Therefore, the differential of the given function is $\frac{e^{x/10}}{10}dx$ .

(b)

To determine

To find: The value of $dy$ and $\Delta y$ .

Answer to Problem 25E

The value of $dy$ is $0.01$ and $\Delta y$ is $0.0101$ .

Explanation of Solution

Given information:

The given function is,

  $y=e^{x/10}$

The differential of the given function is calculated as,

  $\begin{array}{l}y=e^{x/10}\\ dy=\frac{e^{x/10}}{10}dx\\ dy=\frac{e^{0/10}}{10}\left(0.1\right)\\ dy=0.01\end{array}$

The value of $\Delta y$ is calculated as,

  $\begin{array}{c}\Delta y=e^{0.1/10}-e^{0/10}\\ =0.0101\end{array}$

Therefore, the value of $dy$ is $0.01$ and $\Delta y$ is $0.0101$ .