mth 261 module 1 exam (sec 1.1 - 1.8) - form 1-21-a (honorlock) started: apr 6 at 6:36pm quiz instructions…

Explanation:

Step1: Recall power - rule for derivatives

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=nax^{n - 1}$.

Step2: Find the first - derivative

Given $y = 4x^5-3x^2 - 4x + 1$. Using the power - rule, $\frac{dy}{dx}=\frac{d}{dx}(4x^5)-\frac{d}{dx}(3x^2)-\frac{d}{dx}(4x)+\frac{d}{dx}(1)=20x^4-6x - 4$.

Step3: Find the second - derivative

Differentiate $\frac{dy}{dx}$ with respect to $x$. $\frac{d^2y}{dx^2}=\frac{d}{dx}(20x^4)-\frac{d}{dx}(6x)-\frac{d}{dx}(4)=80x^3-6$.

Step4: Find the third - derivative

Differentiate $\frac{d^2y}{dx^2}$ with respect to $x$. $\frac{d^3y}{dx^3}=\frac{d}{dx}(80x^3)-\frac{d}{dx}(6)=240x^2$.

Step5: Find the fourth - derivative

Differentiate $\frac{d^3y}{dx^3}$ with respect to $x$. $\frac{d^4y}{dx^4}=\frac{d}{dx}(240x^2)=480x$.

Answer:

$480x$