Differentiate each of the following functions from the first principal :

log cos x

We have to find the derivative of log cosx with the first principle method, so,

f(x) = log cos x


by using the first principle formula, we get,


f ‘(x) =


f ‘(x) =


f ‘(x) =


f ‘(x) =


[Adding and subtracting 1]


f ‘(x) =


[Rationalising]


f ‘(x) =


[By using limx0 = 1]


f ‘(x) =


[cosC – cosD = –2 sin sin]


f ‘(x) = [By using limx0 = 1]


f ‘(x) =


f ‘(x) = – tan x


6