Differentiate the following function w.r.t. x:

(x)^{cos x} + (sin x)^{tan x}

formula: -

given: -

y = (x)cos x + (sin x)tan x

Let u = x^cosx

taking log both sides

log u = cos x. log x

now diff.w.r.to x

……………………(i)

let v = sin x^tanx

taking log both sides,

log v = tan x log sin x

diff. w.r.t x, get

--------------(ii)

Adding both (i) and (ii)

= sin x^tanx {1+sec² x. log sin x}