Differentiating lnsecx: -pi/2 <= x <= 0

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Homework Help Overview

The discussion revolves around differentiating the function y = ln(sec(x)) within the interval -π/2 ≤ x ≤ 0. Participants are exploring the application of calculus techniques to find the derivative dy/dx.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants consider using the product rule and chain rule for differentiation. There is mention of a substitution u = sec(x) as a potential approach. Some express uncertainty about the correct method to apply.

Discussion Status

There are various attempts to clarify the differentiation process, with some participants providing hints and others suggesting specific methods. The discussion includes a mix of guidance and questions about the appropriate techniques to use, without reaching a consensus on a single approach.

Contextual Notes

Some participants note the importance of adhering to forum guidelines by avoiding complete solutions, indicating a focus on learning through hints and discussion.

thomas49th
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Homework Statement


Given that y = lnsecx, - pi/2 <=x<=0, use the substituation u = secx, or otherwise, to show that dy/dx = tan x.

The Attempt at a Solution



well i thought about using the product rule, but you as it's ln(secx) not lnxsecx (2 different functions)... soooo I am all out of ideas :(

Thanks :)
 
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You could probably use chain rule...as in:

<< complete solution deleted by berkeman >>

Don't quote me on this, I'm still learning basic calculus.=D
 
Last edited by a moderator:
DMac said:
You could probably use chain rule...

DMac,

FYI, it's preferable to just give hints, like the part I quoted above, rather than give complete solutions as you did.

Regards,

Mark
 
Hi thomas49th! :smile:

The question says:
thomas49th said:
… use the substituation u = secx …

So try it … u = secx, so du = … ?, and y = … ? :smile:
 
chain rule:

dy/dx = dy/du . du/dx

dy/du of lnsecx = 1/secx

du/dx = secxtanx

1/secx . secxtanx = tanx

Cheers :)
 
Whoops sry guys, I'm still relatively new to the forum. My apologies.
 
DMac said:
Whoops sry guys, I'm still relatively new to the forum. My apologies.

urrh …I was asleep! :zzz:

Listen for the snoring next time!
 

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