Chapter 4, Problem 31RE

To determine

To calculate: The derivative of y with respect to x .

Answer to Problem 31RE

The domain is $\left\{x\in R:x\ne 0\right\}$ .

Explanation of Solution

Given information: The equation is given as,

  $y=\ln x^2$

Calculation: Using the differentiation,

  $\begin{array}{l}y=\ln x^2\\ \text{On Differentiating with respect to x,}\\ \frac{dy}{dx}=\frac{d\left(\ln x^2\right)}{dx}\\ \frac{dy}{dx}=2\times \frac{d}{dx}\left[\ln x\right]\\ \frac{dy}{dx}=\frac{2}{x}\end{array}$

The domain is where the function is eligible to be solved,

So, the domain is $\left\{x\in R:x\ne 0\right\}$ .