# How do you differentiate #y= (1- sec x)/ tan x#?

Let's see how.

The Quotient Rule:

Multiply some things together:

Get rid of extra parentheses:

Move things around a bit (you'll see why soon):

Nice, now we can cancel more out!

And now we're done!

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To differentiate ( y = \frac{{1 - \sec(x)}}{{\tan(x)}} ):

- Identify ( u(x) ) as ( 1 - \sec(x) ) and ( v(x) ) as ( \tan(x) ).
- Apply the quotient rule formula: ( y' = \frac{{u'v - uv'}}{{v^2}} ).
- Find ( u'(x) ) by differentiating ( 1 - \sec(x) ) and ( v'(x) ) by differentiating ( \tan(x) ).
- Substitute the values into the formula and simplify to get ( y' ).

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