Chapter 4.4, Problem

To determine

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

Answer

The derivative is $\frac{dy}{dx}=\frac{1}{x}$ .

Explanation of Solution

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

  $y=\ln 2\times {\log }_{2}x$

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

Calculation: Using the derivation,

  $\begin{array}{l}y=\ln 2\times {\log }_{2}x\\ y=\ln 2\times \frac{\ln x}{\ln 2}\\ y=\ln x\\ \frac{dy}{dx}=\frac{1}{x}\end{array}$

So the derivative is $\frac{dy}{dx}=\frac{1}{x}$ .