Chapter 3.3, Problem 3E

To determine

To calculate: The value of $\frac{dy}{dx}$ .

Answer to Problem 3E

The required value of $\frac{dy}{dx}$ is 2.

Explanation of Solution

Given information:

The expression: $y=2x+1$

Formula used:

Sum rule:

  $\frac{d}{dx}\left(f+g\right)=\frac{d}{dx}\left(f\right)+\frac{d}{dx}\left(g\right)$

Calculation:

The given expression is $y=2x+1$ .

To find the value of $\frac{dy}{dx}$ , use the sum rule.

  $\begin{array}{c}\frac{dy}{dx}=\frac{d}{dx}\left(2x+1\right)\\ =\frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(1\right)\\ =2\frac{d}{dx}\left(x\right)+0\end{array}$

Simplify the above expression further.

  $\begin{array}{c}2\frac{d}{dx}\left(x\right)+0=2\cdot \left(1\right)\\ =2\end{array}$

Hence, the required value of $\frac{dy}{dx}$ is 2.