Differentiate the following functions from first principles :

ecos x

We have to find the derivative of ecos x with the first principle method, so,

f(x) = ecos x


by using the first principle formula, we get,


f ‘(x) =


f ‘(x) =


f ‘(x) =


f ‘(x) =


[By using = 1]


f ‘(x) =


f ‘(x) =


[By using cos(x+h) = cosx cosh – sinx sinh]


f ‘(x) =


[By using limx0 = 1 and


cos 2x = 1–2sin2 x]


f ‘(x) =


f ‘(x) =


f ‘(x) = –ecos x sin x


4