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: \[ f^{\prime}(x)=\square \quad \square(x)=\frac{4 \tan x}{x} . \] \[ f^{\prime}(5)= \]
failed

Solution

failed
failed

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: \[ \boxed{-2.7044} \]

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Give the domain and range. Then, use the graph to find (a) f(-3), (b) f(0), (c) f(1), and (d) any values of x such that f(x)=3. (b) f(0)= (Type an integer or a decimal.) (c) f(1)= (Type an integer or a decimal.) (d) What are the values of x for which f(x)=3? (Use a comma to separate answers as needed.)
failedAnswered
component of 4.1 × 10^-5 T
failedAnswered
Consider the following quadratic equation: 15 x^2=16 x+7 Step 2 of 2 : Solve the quadratic equation by factoring. Write your answer in reduced fraction form, if necessary. Answer x=
failedAnswered
Why would reading about positive characters of your own ethnicity build confidence? It helps you realize your abilities. It makes you feel curious. It makes you highly generous. It helps you be more realistic.
failedAnswered
If cells are placed in an isotonic solution, Multiple Choice water diffuses out of the cells, and the cells shrink in a process called hemolysis water diffuses out of the cells, and the cells shrink in a process called crenation water diffuses into the cells and the cells swell, and eventually burst in a process called hemolysis water diffuses into the cells and the cells swell, and eventually burst in a process called crenation water diffuses in and out of the cells at the same rate, and the cells remain the same size