question 11 (bonus) (2 points) extra credit: (you may skip this question without losing any points)…

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$, and the derivative of a sum/difference of functions is the sum/difference of their derivatives.

Step2: Differentiate each term

For the term $4x^{2}$, using the power - rule with $a = 4$ and $n = 2$, we have $(4x^{2})^\prime=4\times2x^{2 - 1}=8x$. For the term $5x$, using the power - rule with $a = 5$ and $n = 1$, we have $(5x)^\prime=5\times1x^{1 - 1}=5$. For the term $-2$ (a constant), the derivative of a constant $c$ is $0$, so $(-2)^\prime = 0$.

Step3: Combine the derivatives

The derivative of $y = 4x^{2}+5x - 2$ is $y^\prime=(4x^{2})^\prime+(5x)^\prime+(-2)^\prime=8x + 5+0$.

Answer:

$8x + 5$