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

[thomas49th]

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 :)

 

[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

 

[Redbelly98]

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

 

[tiny-tim]

Hi thomas49th!

The question says:

… use the substituation u = secx …

So try it … u = secx, so du = … ?, and y = … ?

 

[thomas49th]

chain rule:

dy/dx = dy/du . du/dx

dy/du of lnsecx = 1/secx

du/dx = secxtanx

1/secx . secxtanx = tanx

Cheers :)

 

[DMac]

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

 

[tiny-tim]

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

urrh …I was asleep! :zzz:

Listen for the snoring next time!