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

1 Answer
sente
Dec 24, 2015

Simplify the expression before differentiating to find
f'(x) = cscxcotxf'(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 = -cscxcotxddxcscx=−cscxcotx

f'(x) = d/dx (1-secx/tanx)f'(x)=ddx(1−secxtanx)

= d/dx(1-(1/cosx)/(sinx/cosx))=ddx(1−1cosxsinxcosx)

= d/dx (1-1/sinx)=ddx(1−1sinx)

= d/dx(1-cscx)=ddx(1−cscx)

= cscxcotx=cscxcotx

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