Question

attempt 1: 10 attempts remaining. use the rules of derivatives to calculate the derivative of the following function and simplify if possible. do not round. $g(x)=3e^{x}-9x - 3$ $g(x)=$

Explanation:

Step1: Apply derivative rules

The derivative of $e^x$ is $e^x$ and the derivative of $ax$ (where $a$ is a constant) is $a$, and the derivative of a constant is 0.

Step2: Differentiate each term

For the first - term $3e^x$, using the constant - multiple rule $(cf(x))'=cf'(x)$ where $c = 3$ and $f(x)=e^x$, its derivative is $3e^x$. For the second - term $-9x$, its derivative is $-9$. For the third - term $-3$ (a constant), its derivative is 0.

Step3: Combine the derivatives

$g'(x)=3e^x-9 + 0$.

Answer:

$3e^x-9$