Question

The divergence of the vector field $\overrightarrow{u}=e^x(cosy\hat{i}+siny\hat{j})$ is

• A. 0
• B. $e^{x}cosy+e^{x}siny$
• C. $2e^{x}cosy$
• D. $2e^{x}siny$

Answer 1

The correct option is C $2e^{x}cosy$

$\overrightarrow{u}=\left(e^{x}cosy\right)\hat{i}+\left(e^{x}siny\right)\hat{j}$
$div\overrightarrow{u}=\left(\frac{\partial u}{\partial x}\right)+\left(\frac{\partial u}{\partial y}\right)+\left(\frac{\partial u}{\partial z}\right)$
$=e^{x}cosy+e^{x}cosy+0=2e^{x}cosy$