Question

question: find the derivative of (f(x)=3x^{3}+5x^{2}+5). provide your answer below. (f(x)=square)

Explanation:

Step1: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$, and the derivative of a constant $C$ is $0$. For $f(x)=3x^3 + 5x^2+5$, the derivative of $3x^3$ is $3\times3x^{3 - 1}$, the derivative of $5x^2$ is $5\times2x^{2 - 1}$, and the derivative of $5$ is $0$.
$3\times3x^{3 - 1}+5\times2x^{2 - 1}+0$

Step2: Simplify the expression

$9x^{2}+10x$

Answer:

$f^\prime(x)=9x^{2}+10x$