Question

question find the derivative of the function f(x)=x^2 + 4x + 9. provide your answer below: f(x)=□

Explanation:

Step1: Apply power - rule

The power - rule states that if $y = x^n$, then $y^\prime=nx^{n - 1}$. For the function $f(x)=x^{2}+4x + 9$, we differentiate each term separately.
The derivative of $x^{2}$ using the power - rule: if $n = 2$, then $\frac{d}{dx}(x^{2})=2x^{2-1}=2x$.

Step2: Differentiate linear term

The derivative of $4x$: since $y = 4x=4x^{1}$, using the power - rule with $n = 1$, we have $\frac{d}{dx}(4x)=4\times1\times x^{1 - 1}=4$.

Step3: Differentiate constant term

The derivative of a constant $C$ (in this case $C = 9$) is 0, i.e., $\frac{d}{dx}(9)=0$.

Step4: Sum up the derivatives

$f^\prime(x)=\frac{d}{dx}(x^{2})+\frac{d}{dx}(4x)+\frac{d}{dx}(9)=2x + 4+0$.

Answer:

$2x + 4$