What is the derivative of natural log with exponents?

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Discussion Overview

The discussion revolves around understanding the derivatives of functions involving exponents, specifically focusing on the function f(x) = 7^8^x. Participants explore different interpretations of the function and the application of differentiation rules.

Discussion Character

  • Exploratory, Technical explanation, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about finding the derivative of f(x) = 7^8^x and requests help.
  • Another participant clarifies the potential interpretations of the function, suggesting two forms: a) f(x) = (7^{8})^{x} and b) f(x) = 7^{8^x}.
  • A participant indicates they are working on the second interpretation (b) and suggests using the chain rule of differentiation with u(x) = 8^{x}.
  • Another participant introduces a related question about differentiating the quotient of two exponential functions, specifically 3^x/4^x, and inquires about the rules of differentiation applicable in this case.
  • One participant suggests rewriting the quotient as (3/4)^{x} to simplify the differentiation process.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the function f(x) = 7^8^x, as multiple interpretations are presented. The discussion includes various approaches to differentiation without resolving the initial confusion.

Contextual Notes

Participants' understanding of the function's structure and the application of differentiation rules may depend on their interpretations, which remain unresolved. There is also a lack of clarity on the specific rules applicable to the differentiation of the quotient presented.

Who May Find This Useful

Students or individuals seeking assistance with derivatives involving exponential functions, particularly those with complex structures or quotients.

mavsqueen06
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Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=?
help please!
 
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Are you talking of:
a) f(x)=(7^{8})^{x}
b) f(x)=7^{8^x}
 
mavsqueen06 said:
Having some trouble understanding derivatives including numbers to the "X" power. For example, f(x)= 7^8^x, f'(x)=?
help please!

You should find this link useful: "[URL .[/URL]
 
Last edited by a moderator:
i'm working on the B) one
 
So, set u(x)=8^{x}, and use the chain rule of differentiation.
 
ok, thanks, what about dividing them? do i still use rules of differentiation. for example, 3^x/4^x
 
Or, use first:
\frac{3^{x}}{4^{x}}=(\frac{3}{4})^{x}
 
thanks so much!
 

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