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 limx→0 = 1]
f ‘(x) = – cot x