Differentiate lnsecx

1. Jun 5, 2008

thomas49th

1. The problem statement, all variables and given/known data
Given that y = lnsecx, - pi/2 <=x<=0, use the substituation u = secx, or otherwise, to show that dy/dx = tan x.

3. 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 im all out of ideas :(

Thanks :)

2. Jun 5, 2008

DMac

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: Jun 5, 2008
3. Jun 5, 2008

Redbelly98

Staff Emeritus
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

4. Jun 5, 2008

tiny-tim

Hi thomas49th!

The question says:
So try it … u = secx, so du = … ?, and y = … ?

5. Jun 5, 2008

thomas49th

chain rule:

dy/dx = dy/du . du/dx

dy/du of lnsecx = 1/secx

du/dx = secxtanx

1/secx . secxtanx = tanx

Cheers :)

6. Jun 6, 2008

DMac

Whoops sry guys, I'm still relatively new to the forum. My apologies.

7. Jun 6, 2008

tiny-tim

urrh …I was asleep! :zzz:

Listen for the snoring next time!

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