Question

How do you differentiate `f(x) =1- sec x/ tan x`?

Answer 1

Simplify the expression before differentiating to find
`f'(x) = cscxcotx`

Explanation:

Sometimes, an expression may be simplified before differentiating to make the task easier. We use this, along with the derivative
`d/dxcscx = -cscxcotx`

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`f'(x) = d/dx (1-secx/tanx)`

`= d/dx(1-(1/cosx)/(sinx/cosx))`

`= d/dx (1-1/sinx)`

`= d/dx(1-cscx)`

`= cscxcotx`