How to derive a number to the power x (e.g. 2^x)

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Discussion Overview

The discussion revolves around the differentiation of exponential functions, specifically focusing on the derivatives of expressions like 2^x and x^x. The scope includes calculus concepts and techniques relevant to these types of derivatives.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about deriving functions of the form a^x, such as 2^x, and x^x, seeking assistance or resources.
  • Another participant suggests using logarithmic differentiation as a method to derive x^x, explaining the process involving natural logarithms and the chain and product rules.
  • A repeated post reiterates the initial confusion about deriving 2^x and x^x, indicating a need for clarification.
  • A participant acknowledges the help received, indicating that the provided information was useful.

Areas of Agreement / Disagreement

The discussion does not present a consensus, as it primarily consists of a request for help and a suggested method without further exploration of alternative approaches or solutions.

Contextual Notes

There may be limitations in the assumptions made about the participants' familiarity with calculus concepts, and the discussion does not delve into the details of the logarithmic differentiation method or its applicability to different types of exponential functions.

develish16
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i recently started my calculus III course but i was stuck with the derivative part when i derive a real number to the power x ( like 2^x) and also when deriving x^x. does anybody have an idea or a link in which these kinds of derivatives can be solved. thanks for ur help
 
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Use "logarithmic differentiation". If [itex]y= x^x[/itex], then [itex]ln(y)= ln(x^x)= xln(x)[/itex]. Use the chain rule to differentiate ln(y) with respect to x (y'/y) and use the product rule on the right. Then solve for y'.
 
develish16 said:
i recently started my calculus III course but i was stuck with the derivative part when i derive a real number to the power x ( like 2^x) and also when deriving x^x. does anybody have an idea or a link in which these kinds of derivatives can be solved. thanks for ur help

2x = ex ln(2)
 
thx a lot guys that was so helpful
 

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