Solving g(t): Seeking Help with Chain Rule

  • Thread starter Thread starter spherenine
  • Start date Start date
  • Tags Tags
    Chain Chain rule
Click For Summary

Homework Help Overview

The discussion revolves around finding the derivative of the function g(t) = 4ln(5ln(4t)), focusing on the application of the chain rule in calculus.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply the chain rule but expresses uncertainty about the derivative of ln(4t). Some participants confirm the derivative of ln(4t) as 1/t and discuss the subsequent steps in the differentiation process.

Discussion Status

Participants are actively engaging with the problem, providing confirmations and partial derivations. There appears to be a collaborative effort to clarify the steps involved in applying the chain rule, though no consensus on a final answer is reached.

Contextual Notes

There is an indication of reliance on an answer key, which may influence the discussion dynamics. The original poster seeks guidance without providing complete solutions, adhering to homework help norms.

spherenine
Messages
5
Reaction score
0

Homework Statement



g(t) = 4ln(5ln(4t))

Homework Equations



What is the derivative of g(t)?

The Attempt at a Solution



I have tried to use the chain rule in many different ways, and still can't come up with the correct answer. Anybody care to walk me through this? Is the derivative of ln(4t) still 1/t?
 
Physics news on Phys.org
(ln(4t))'=(1/(4t))*4=1/t. Yes. It's still 1/t. For your problem g'=4*(1/(5*ln(4t)) times the derivative of 5*ln(4t). What do you make it?
 
4*(1/(5*ln(4t)) = 4/(5*ln(4t))
Deriv 5*ln(4t) = 5/t

5/t * 4/(5*ln(4t)) = 20/(5t*ln(4t)) = 4/(t*ln(4t)) =

4*(ln(4t))^-1*t^-1?
 
I agree with that.
 
So does the answer key. Thanks for your help.
 

Similar threads

Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
2
Views
2K
Replies
2
Views
1K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K