for the following equation, evaluate $\frac{dy}{dx}$ when $x = 4$.\n$y=-4x^{2}-2x$

Explanation:

Step1: Differentiate the function

Using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, if $y=-4x^{2}-2x$, then $\frac{dy}{dx}=\frac{d}{dx}(-4x^{2})+\frac{d}{dx}(-2x)$. $\frac{dy}{dx}=-4\times2x-2=-8x - 2$.

Step2: Substitute $x = 4$

Substitute $x = 4$ into $\frac{dy}{dx}$. $\frac{dy}{dx}\big|{x = 4}=-8\times4-2$. $\frac{dy}{dx}\big|{x = 4}=-32 - 2=-34$.

Answer:

$-34$