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

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

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Solution Steps

Step 1: Identify the Function and Its Form

The given function is f(x)=3x3 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)=axn f(x) = ax^n , then f′(x)=anxn−1 f^{\prime}(x) = anx^{n-1} .

Step 3: Differentiate the Function

Using the power rule, differentiate f(x)=3x3 f(x) = 3x^3 :

f′(x)=3⋅3x3−1=9x2 f^{\prime}(x) = 3 \cdot 3x^{3-1} = 9x^2

Final Answer

The derivative of the function is:

f′(x)=9x2 \boxed{f^{\prime}(x) = 9x^2}

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