Differentiation of Trigonometric functions

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Homework Help Overview

The problem involves finding the derivative of the function y = tan²(3x-2). Participants are discussing the differentiation of trigonometric functions, specifically focusing on the application of the chain rule and the correct form of the derivative.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to differentiate the function and are questioning the correctness of the derivative provided. There is a discussion about the application of the power rule and the chain rule in this context.

Discussion Status

Some participants have offered insights into the differentiation process, while others are clarifying terminology and expressing confusion about the notation used. There is an ongoing exploration of the derivative's form without a clear consensus on the correct approach yet.

Contextual Notes

There are informal exchanges among participants wishing each other a happy new year, which may indicate a casual atmosphere. Some participants are also clarifying terms used in the discussion, such as "parenthesis."

MaxManus
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Homework Statement


Let y = tan2(3x-2)
Find dy/dx


The solution is:
2*tan(3x-2)*sec(3x-2)*3
= 6*tan(3x-2)*sec2(3x-2)

Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))2
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Edit: Happy new year
 
Physics news on Phys.org
happy new year!

MaxManus said:
Let y = tan2(3x-2)
Find dy/dx
…
Why is it not:
6*tan(3x-2)*sec(3x-2)

I am thinking:
y = (tan(3x-2))2
take the power 2 down,multiply with the parentes multiply with the defferentiated parentes

Hi MaxManus! Happy new year! :smile:

(what are parentes? :confused: do you mean "parenthesis"?)

y = (thing)2,

so y' = 2(thing)(thing') …

in this case, the thing is a tan, and tan' = sec2 :wink:
 
What do you think d(tan(u))/dx is equivalent to?

Edit: tiny-tim beat me to it.
 
happy new year!

jgens said:
Edit: tiny-tim beat me to it.

na na na na-na! :-p

hic! :redface:

:smile: happy new year! :smile:​
 
Happy new year! :)
 
Thanks tiny-tim and jgens.
Yes, I ment parenthesis, but I could not spell it.
 
Hitting the champagne a little early?
 

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