Chapter 4, Problem 12RE

To determine

The derivative of the given function.

Answer to Problem 12RE

The derivative is $\frac{1}{2x}$ .

Explanation of Solution

Given information: Given function $y=\ln \sqrt{x}$

Formula used: $\frac{d(\ln x)}{dx}=\frac{1}{x}\text{and}\frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}$ with chain rule.

Calculation:

  $\begin{array}{l}y=\ln \sqrt{x}\\ \text{Differentiate}\text{with}\text{respect}\text{to}x\\ \frac{dy}{dx}=\frac{d(\ln \sqrt{x})}{d(\sqrt{x})}\times \frac{d(\sqrt{x})}{dx}\\ \frac{dy}{dx}=\frac{1}{\sqrt{x}}\times \frac{1}{2\sqrt{x}}\\ \frac{dy}{dx}=\frac{1}{2x}\end{array}$