Question

differentiate the function.
f(x) = e^9
f(x) = 9e^9 x
resources
read it
submit answer

1. -/1 points

differentiate the function.
g(x) = 3x + 4
g(x) =
resources
read it watch it

Explanation:

Step1: Recall derivative rules

The derivative of a constant $c$ with respect to $x$ is 0, i.e., $\frac{d}{dx}(c)=0$. Since $e^{9}$ is a constant (because $e\approx2.718$ and $e^{9}$ is a fixed - value number), for $f(x)=e^{9}$, $f^{\prime}(x) = 0$.

Step2: Recall derivative rules for linear function

For a linear function $g(x)=ax + b$ where $a$ and $b$ are constants, the derivative $\frac{d}{dx}(ax + b)=a$ (using the power rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$, and $\frac{d}{dx}(b)=0$). For $g(x)=3x + 4$, $a = 3$ and $b = 4$, so $g^{\prime}(x)=3$.

Answer:

$f^{\prime}(x)=0$
$g^{\prime}(x)=3$