Questions: Find f'(x) for the given function. f(x)=4 x^3 f'(x)=

Find f'(x) for the given function. f(x)=4 x^3 f'(x)=
Transcript text: Find $f^{\prime}(x)$ for the given function. \[ f(x)=4 x^{3} \] \[ f^{\prime}(x)= \]
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Solution

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Solution Steps

Step 1: Identify the function

The given function is \( f(x) = 4x^{3} \).

Step 2: Apply the power rule

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

Step 3: Compute the derivative

Using the power rule, the derivative of \( f(x) = 4x^{3} \) is: \[ f^{\prime}(x) = 4 \cdot 3 \cdot x^{3-1} = 12x^{2}. \]

Final Answer

\(\boxed{f^{\prime}(x) = 12x^{2}}\)

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