Questions: Find f'(x) for f(x)=3x^3.

Find f'(x) for f(x)=3x^3.
Transcript text: Find $f^{\prime}(x)$ for $f(x)=3 x^{3}$.
failed

Solution

failed
failed

Solution Steps

Step 1: Identify the Function and Its Form

The given function is \( f(x) = 3x^3 \). This is a polynomial function, and we need to find its derivative.

Step 2: Apply the Power Rule

The power rule for differentiation states that if \( f(x) = ax^n \), then \( f^{\prime}(x) = anx^{n-1} \).

Step 3: Differentiate the Function

Using the power rule, differentiate \( f(x) = 3x^3 \):

\[ f^{\prime}(x) = 3 \cdot 3x^{3-1} = 9x^2 \]

Final Answer

The derivative of the function is:

\[ \boxed{f^{\prime}(x) = 9x^2} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Use the function below to answer parts (a)-(d). f(x) = (5/2) x^2 (a) Graph the function (b) Draw lines tangent to the graph at points whose x-coordinates are 0, and 1,3. (c) Find f'(x) by determining lim (f(x+h)-f(x))/h. (d) Find f'(0), f'(1), and f'(3).
failedAnswered
Which of the following statements describes liabilities? a.) Lauren can claim ownership of the restaurant equipment and delivery vehicles, totaling 28,000. b.) The profits of all three of Karen's pizzerias total 162,000. c.) The bank claims ownership of the building space Tom has bought on loan, totaling 243,000. d.) Barry spends 38,000 annually on advertising to increase profits.
failedAnswered
What is the slope of this line? 5/3 -5/3
failedAnswered
Which of the following is not a unit of measurement for area? Square feet in^3 Square inches ft^2
failedAnswered
Evaluate the definite integral. Use a graphing utility to verify your result. (Round your answer to three decimal places.) ∫ from 0 to 4 of x e^(x / 3) dx