Questions: f'(x)= square square(x)= 4 tan x / x . f'(5)=

f'(x)= square square(x)= 4 tan x / x . f'(5)=
Transcript text: \[ f^{\prime}(x)=\square \quad \square(x)=\frac{4 \tan x}{x} . \] \[ f^{\prime}(5)= \]
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Solution

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Solution Steps

To solve this problem, we need to evaluate the derivative of the function \( f(x) \) given that its derivative is expressed as \( f^{\prime}(x) = \frac{4 \tan x}{x} \). We are specifically asked to find the value of \( f^{\prime}(5) \). This involves substituting \( x = 5 \) into the derivative function and calculating the result.

Step 1: Define the Derivative Function

We are given the derivative of the function \( f(x) \) as: \[ f^{\prime}(x) = \frac{4 \tan x}{x} \]

Step 2: Substitute \( x = 5 \)

To find \( f^{\prime}(5) \), we substitute \( x = 5 \) into the derivative function: \[ f^{\prime}(5) = \frac{4 \tan(5)}{5} \]

Step 3: Calculate the Value

Using the value of \( \tan(5) \), we compute: \[ f^{\prime}(5) \approx -2.7044 \]

Final Answer

Thus, the value of \( f^{\prime}(5) \) is approximately: \[ \boxed{-2.7044} \]

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