question: find the derivative of (f(x)=3x^{3}+5x^{2}+5). provide your answer below. (f(x)=square)
question: find the derivative of (f(x)=3x^{3}+5x^{2}+5). provide your answer below. (f(x)=square)
Answer
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:
$f^\prime(x)=9x^{2}+10x$