# Nth derivative, differentiation

• D678
In summary, the Nth derivative of a function is the derivative of the derivative of the function, N times. It is calculated using various derivative rules and has significance in mathematics for studying function behavior and identifying patterns. The Nth derivative can be negative, indicating a decreasing rate of change. In real-world applications, it is used in fields such as physics, engineering, economics, and finance for modeling and optimization purposes.
D678

## Homework Statement

Find f^n for f(x) = Ln(2x+1)

Can anyone point me in the right direction with how to get the nth derivative of the above function please, I just cannot seem to work this out!

Thank you

I would start by finding f',f'' and maybe f''', perhaps a pattern will emerge.

This is obviously a calculus problem, so should be posted in Calculus & Beyond. I am moving it to that section.

## 1. What is an Nth derivative?

The Nth derivative of a function is the derivative of the derivative of the function, N times. It represents the rate of change of the rate of change of the function.

## 2. How is the Nth derivative calculated?

The Nth derivative is calculated by taking the derivative of the function N times, using the power rule, product rule, quotient rule, and chain rule as needed.

## 3. What is the significance of the Nth derivative in mathematics?

The Nth derivative is significant in mathematics because it allows us to find the rate of change of a function at different levels of precision. It also helps us study the behavior of a function and identify patterns and relationships between the function and its derivatives.

## 4. Can the Nth derivative be negative?

Yes, the Nth derivative can be negative. This indicates that the rate of change of the function is decreasing at a particular point.

## 5. How is the Nth derivative used in real-world applications?

The Nth derivative is used in various fields such as physics, engineering, economics, and finance to model and analyze the behavior of systems and functions. It is also used in optimization problems to find maximum or minimum values of a function.

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