Chapter 3.3, Problem 1E

To determine

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

Answer to Problem 1E

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

Explanation of Solution

Given information:

The expression: $y=-x^2+3$

Formula used:

Sum rule:

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

Calculation:

The given expression is $y=-x^2+3$ .

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

  $\begin{array}{c}\frac{dy}{dx}=\frac{d}{dx}\left(-x^2+3\right)\\ =\frac{d}{dx}\left(-x^2\right)+\frac{d}{dx}\left(3\right)\\ =-2x+0\\ =-2x\end{array}$

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