What is the Quotient Rule for Calculating Derivatives?

In summary, "f(x)" stands for the function used in an equation to show the relationship between the input and output. It is different from "x" as it represents the output value after the input has been plugged into the function. "f(x)" can be used with any type of function and is sometimes written as "y" to represent the output value. In real-life applications, "f(x)" is used to model and make predictions based on different variables.
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CynicusRex
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Homework Statement


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Homework Equations


The Quotient rule for calculating the derivative.

The Attempt at a Solution


The derivative f'(x) = (x+5)-(x+3) / (x+5)^2
I tried a previous similar problem but failed as I didn't and still don't know what '' means.
 
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  • #2
##f''(x)## is the derivative of ##f'(x)##.
 
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f"(x) is the second derivative of f(x)
 
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Thank you both.
 

1. What is the meaning of "f" in "f(x)"?

The "f" in "f(x)" stands for the function that is being used in the equation. It is a placeholder for any function and is used to show the relationship between the input (x) and the output (f(x)).

2. How is "f(x)" different from "x" in an equation?

"x" represents the input value in an equation, while "f(x)" represents the output value after the input has been plugged into the function. Essentially, "x" is the independent variable and "f(x)" is the dependent variable.

3. Can "f(x)" be used with any type of function?

Yes, "f(x)" can be used with any type of function, whether it is linear, quadratic, exponential, etc. It is a general notation to represent a function and can be used in various mathematical contexts.

4. Why is "f(x)" sometimes written as "y" in equations?

In some cases, "f(x)" may be written as "y" in equations to represent the output value of the function. This is commonly seen in algebraic equations, where "y" is used as the dependent variable and "x" is used as the independent variable.

5. How is "f(x)" used in real-life applications?

"f(x)" is used in various real-life applications, such as calculating the trajectory of a projectile, predicting population growth, and modeling financial investments. It allows us to represent the relationship between different variables and make predictions or analyze data.

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