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 limx→0 = 1 and
cos 2x = 1–2sin2 x]
f ‘(x) =
f ‘(x) =
f ‘(x) = –ecos x sin x