Question

find the value of the derivative.
$left.\frac{dy}{dx}
ight|_{x = - 4}$ if $y = 4-5x^{2}$
$left.\frac{dy}{dx}
ight|_{x = - 4}=square$ (simplify your answer.)

Explanation:

Step1: Differentiate the function

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$ and $\frac{d}{dx}(c)=0$ (where $c$ is a constant), for $y = 4-5x^{2}$, we have $\frac{dy}{dx}=\frac{d}{dx}(4)-5\frac{d}{dx}(x^{2})$. Since $\frac{d}{dx}(4) = 0$ and $\frac{d}{dx}(x^{2})=2x$, then $\frac{dy}{dx}=0 - 5\times2x=-10x$.

Step2: Evaluate the derivative at $x = - 4$

Substitute $x=-4$ into $\frac{dy}{dx}$. We get $\frac{dy}{dx}\big|_{x = - 4}=-10\times(-4)$.

Answer:

40