Answer :
We have to find the derivative of log cosec x with the first principle method, so,
f(x) = log cosecx
by using the first principle formula, we get,
f ‘(x) = 
f ‘(x) = 
f ‘(x) = 
f ‘(x) = 
[By using log a – log b = log 
]
f ‘(x) = 
[adding and subtracting 1]
f ‘(x) = 
f ‘(x) = 
[Rationalising]
f ‘(x) = 
f ‘(x) = 
[sin C – sin D = 2 sin 
cos
]
f ‘(x) = 
[By using limx→0
= 1]
f ‘(x) = – cot x
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