Chapter 4.4, Problem 60E

To determine

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

Answer to Problem 60E

The domain is $\left\{x\in R:x\ne -3\right\}$ . So, option (C) is correct.

Explanation of Solution

Given information: The equation is given as,

  $f(x)={\log }_2(x+3)$

Calculation: Using the differentiation,

  $\begin{array}{l}f(x)={\log }_2(x+3)\\ \text{On Differentiating with respect to x,}\\ \frac{d(f(x))}{dx}=\frac{d\left({\log }_2(x+3)\right)}{dx}\\ \frac{d(f(x))}{dx}=\frac{1}{\ln (2)}\times \frac{d}{dx}\left[\ln (x+3)\right]\\ \frac{d(f(x))}{dx}=\frac{1}{\ln (2)}\times \frac{1}{(x+3)}\frac{d(x+3)}{dx}\\ \frac{d(f(x))}{dx}=\frac{1}{\ln (2)}\times \frac{1}{(x+3)}\end{array}$

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

So, the domain is $\left\{x\in R:x\ne -3\right\}$ .