Chapter 4.4, Problem 15E

To determine

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

Answer to Problem 15E

The derivative is $\frac{dy}{dx}=\frac{2}{x}$ .

Explanation of Solution

Given information: The equation of y in terms of x is given as,

  $y=\ln \left(x^2\right)$

Formula Used: $\frac{d\left(x^n\right)}{dx}=n\times x^{\left(n-1\right)}$

Calculation: Using the derivation,

  $\begin{array}{l}y=\ln \left(x^2\right)\\ y=2\ln \left(x\right)\\ \frac{dy}{dx}=\frac{d\left(2\ln \left(x\right)\right)}{dx}\\ \frac{dy}{dx}=\frac{2}{x}\end{array}$

So the derivative is $\frac{dy}{dx}=\frac{2}{x}$ .