Why Does Differentiating Arctan(x^2-1) + Arccsc(x) Yield Zero?

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Homework Help Overview

The discussion revolves around the differentiation of the function y = Arctan(x^2-1) + Arccsc(x) for x > 1, with a focus on why the derivative is claimed to be zero according to the textbook answer.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • The original poster expresses confusion regarding the differentiation process and the expected result of zero, despite their calculations yielding a different outcome. Other participants reference a potential relationship involving the inverse tangent and cosecant functions, suggesting a deeper exploration of the functions involved.

Discussion Status

Participants are engaging in a back-and-forth exchange, with some suggesting that the derivative should indeed be zero based on a specific relationship between the functions. However, there is no explicit consensus reached, as the original poster remains uncertain about their calculations.

Contextual Notes

The original poster indicates that this problem is part of a homework assignment, suggesting that there may be constraints on the methods or approaches they can use to solve it.

Simfish
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Hi, I kow about the chain rule and such; but there I cannot solve a problem in my calc textbook.

y = Arctan(x^2-1) + Arccscx, x > 1.

Answer on back says 0; but my answer didn't go to 0. BTW, this is just one problem from a HW assignment so this shouldn't count as cheating.

Thanks!

-Simfish
 
Last edited:
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The derivative should be zero because

[tex]\tan^{-1} \sqrt{x^2-1} + \csc^{-1}x = \frac {\pi}{2}[/tex]
 
Sleazy Tide!
Why didn't I see that..
 
arildno said:
Sleazy Tide!
Why didn't I see that..

LoL! Oh, you would have seen it - I just happened to see it first.
 

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