Chapter 5.5, Problem 19E

To determine

To calculate:

The value of $dy$ and evaluate its value in $y=e^{\sin x}$

Answer to Problem 19E

The value of $dy$ is $\left(\cos x\right)e^{\sin x}dx$ and 0.1 at the given values

Explanation of Solution

Given information:

  $x=\pi$ , $dx=-0.1$

Formula used:

  $\frac{d}{dx}\left(\sin x\right)=cox$

Calculation:

  $\begin{array}{l}y=e^{\sin x}\\ dy=\left(\cos x\right)e^{\sin x}dx\\ dy=\left(\cos \pi \right)e^{\sin \pi }\left(-0.1\right)\\ dy=\left(-1\right)e^{\left(0\right)}\left(-0.1\right)\\ dy=\left(-1\right)\left(1\right)\left(-0.1\right)\\ dy=0.1\end{array}$

Therefore, the value of $dy$ is $\left(\cos x\right)e^{\sin x}dx$ and 0.1 at the given values