Derivative Problem involving Natural Log

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SUMMARY

The discussion focuses on evaluating the derivative of the function p(x) = (5x) - ln(5x). Participants emphasize the necessity of applying the chain rule and introduce the technique of logarithmic differentiation as a viable method for solving the problem. The derivative of ln(x) is noted as 1/x, which is crucial for the differentiation process. The conversation highlights the importance of understanding implicit differentiation when dealing with logarithmic functions.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically derivatives.
  • Familiarity with the chain rule in differentiation.
  • Knowledge of logarithmic functions and their properties.
  • Experience with implicit differentiation techniques.
NEXT STEPS
  • Study the application of the chain rule in more complex functions.
  • Learn about logarithmic differentiation in detail.
  • Practice implicit differentiation with various functions.
  • Explore advanced calculus topics, such as higher-order derivatives.
USEFUL FOR

Students studying calculus, particularly those struggling with differentiation techniques, and educators looking for effective methods to teach logarithmic differentiation.

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Homework Statement



Evaluate the derivative of the following function:

p(x) = (5x)-ln(5x)


Homework Equations



[tex]\frac{d}{dx}[/tex]lnx = [tex]\frac{1}{x}[/tex]
Not sure what else...


The Attempt at a Solution



I know that I will have to use the chain rule in this problem, but actually implementing it is giving me problems. I wish I could give more of an attempt, but I don't really even know where to start. Thanks in advance for the help!
 
Last edited:
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have you heard of the technique 'logarithmic differentiation'? it is where you take the log on both sides and then differentiate implicitly.
 
You could also use the fact that ab is defined as eb log a.
 

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