Trig Differentiation for tan2(4x): Solving 1+tan2(4x) using the Chain Rule

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Homework Help Overview

The discussion revolves around differentiating the expression 1 + tan²(4x) using the chain rule. Participants are exploring the differentiation of trigonometric functions and the application of the chain rule in this context.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the differentiation of the term tan²(4x) and the application of the chain rule. There is a focus on ensuring all components, including the inner function, are differentiated correctly. Some participants question the coefficients involved in the differentiation process.

Discussion Status

The discussion is active, with participants correcting each other and refining their understanding of the differentiation process. There is acknowledgment of mistakes and clarifications regarding the differentiation of the inner function, indicating a collaborative effort to reach a clearer understanding.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the extent of direct solutions provided. The focus remains on understanding the differentiation process rather than arriving at a final answer.

jsmith613
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Homework Statement



how is the differential of 1+tan2(4x)

8*tan(4x)*sec2(4x)

Homework Equations


The Attempt at a Solution


So 1 differentiates to 0 (we can now ignore this)
tan2(4x) differentiates to 2*tan(4x)*sec2(4x)?

BRING POWER FORWARD, DOWN POWER BY 1, DIFFERENTIATE TERM IN BRACKET
by the chain rule?
 
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jsmith613 said:
BRING POWER FORWARD, DOWN POWER BY 1, DIFFERENTIATE TERM IN BRACKET
by the chain rule?


You stated it in your question, but never differentiated the term inside inside the bracket.

[tex]2 \cdot tan(4x)sec^{2}(4x) \cdot \frac{d}{dx} (4x)~=~[/tex]
 
Last edited:
hold on
yours goes to 32...
NOT 8...
 
jsmith613 said:
hold on
yours goes to 32...
NOT 8...

My mistake :-p I fixed it in my first post ( coefficient was originally wrong), but my point still holds. You ALSO need to differentiate the 4x.
 
oh of course
differentiate u2 = 2u
differentiate sec2(4x) is 4*sec(4x)*tan(4x)
multiply differntials to give
2*sec(4x)*4*sec(4x)*tan(4x)
 
Exactly!:approve:
 

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