Differentiate each of the following functions from the first principal :

log cosec x

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 lim_x→0 = 1]

f ‘(x) = – cot x