Differentiate the following functions from first principles :

e^{cos x}

We have to find the derivative of e^{cos x} with the first principle method, so,

f(x) = e^{cos 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 lim_x→0 = 1 and

cos 2x = 1–2sin² x]

f ‘(x) =

f ‘(x) =

f ‘(x) = –e^{cos x} sin x