Calculating the 100th Derivative: Tips & Tricks

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Homework Help Overview

The discussion revolves around calculating the 100th derivative of a function, exploring the patterns that emerge from successive derivatives and how these patterns might relate to higher-order derivatives.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to identify a pattern in the derivatives but struggles to connect it to the 100th derivative. Some participants suggest calculating the first few derivatives to observe any emerging patterns that could assist in finding the nth derivative.

Discussion Status

The discussion is ongoing, with participants sharing insights about derivative patterns and referencing the Leibniz rule as a potential framework for understanding the problem. There is no explicit consensus yet on the best approach to take.

Contextual Notes

Participants are working within the constraints of a homework problem, which may limit the information available for deriving conclusions.

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how would be the best way to do this?

I mean, I know how to find the derivative...

and it kind of makes a pattern...but I can't quite correlate that pattern to the 100th derivative
 
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Find f'(x).then f''(x) and then f'''(x) and see if you find a pattern happening so that you can find the nth derivative of f(x)
 
dammit

ha k thanks
 
y^{(n)}(x) = \sum_{k=0}^n {n \choose k} u^{(n-k)}(x)\; v^{(k)}(x)

This is known as the Leibniz rule (where y(x)=u(x)v(x)).
 

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