Solving y = (3x)^x with the Chain Rule | Homework Help

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Homework Help Overview

The discussion revolves around finding the derivative of the function y = (3x)^x, focusing on the application of the chain rule and properties of exponential functions.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of logarithmic differentiation and implicit differentiation as methods to find the derivative. Questions arise regarding the validity of applying the derivative formula for exponential functions when the base is not a constant.

Discussion Status

Some participants have suggested using logarithmic differentiation, while others are questioning the assumptions behind the derivative formula used. There is an acknowledgment of differing interpretations regarding the application of the formula for a variable base.

Contextual Notes

Participants note that the formula for the derivative of a^x may require 'a' to be a constant, which raises questions about the applicability of the method in this context.

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Homework Statement



y = (3x)^x

(find y' )

Homework Equations



y = a^x
y' = (a^x)(ln(a))

and the chain rule

The Attempt at a Solution



3((3x)^x)(ln(3x))
 
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Take ln of both sides of the equation

lny=x*ln(3x)

Now use implicit differentiation
 
yes, that was the answer that was provided; but I don't understand why my answer is incorrect, given the fact that the derivative of a^x is (a^x)(lin(a)) and the formula seems to be of that form.
 
I believe for that equation to work 'a' must be a constant.
 
O, thanks.
 

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