Simple Calculus Question: Differentiating Square Root Fraction

[nil1996]

Homework Statement

\sqrt{\frac{1-cos2x}{1+cos2x}}
differentiate with respect to x

Homework Equations

none

The Attempt at a Solution

i have simplified it by substituting cos2x as 1-2sin²x and 2cos²x-1

I have got the answer as sec²x but my textbook says the ans is \frac{tanx}{|tanx|}sec²x
why??

please help

 

[rock.freak667]

Your answer is correct. I don't see the need for your book to specify tanx/tanx in it.

 

[nil1996]

I don't see the need for your book to specify tanx/tanx in it.

it is tanx/|tanx|
the denominator is mod of tanx

 

[rock.freak667]

it is tanx/|tanx|
the denominator is mod of tanx

Yes well the main point was that for x>0, |tanx| = tanx so it would cancel out to give you sec²x.

The only reason I can think of to specify something like that is if you accounted for taking the square root of the radical.

Meaning that your expression would simplify to √(tan²x) = ± tanx

and d/dx(± tanx) = ± sec²x

 

[nil1996]

thanks got it