Question

question for the following equation, evaluate $\frac{dy}{dx}$ when $x = 2$. $y=-2x^{3}-5x^{2}-x + 3$

Explanation:

Step1: Differentiate term - by - term

Using the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, we have:
$\frac{dy}{dx}=\frac{d}{dx}(-2x^{3})+\frac{d}{dx}(-5x^{2})+\frac{d}{dx}(-x)+\frac{d}{dx}(3)$
$=-2\times3x^{2}-5\times2x - 1+0$
$=-6x^{2}-10x - 1$

Step2: Substitute $x = 2$

Substitute $x = 2$ into $\frac{dy}{dx}$:
$\frac{dy}{dx}\big|_{x = 2}=-6\times2^{2}-10\times2 - 1$
$=-6\times4-20 - 1$
$=-24-20 - 1$
$=-45$

Answer:

$-45$