Differentiate the following functions with respect to x :
x1+tan x
Let y = x1+tan x
Differentiating y w.r.t. x, we get
dydx=(1+tan x)ddx(x)−xddx(1+tan x)(1+tan x)2
=(1+tan x)(1)−x(0+sec2x)(1+tan x)2
=1+tan x−x sec2x(1+tan x)2
3xx+tan x
x+cos xtan x
ex−tan xcot x−xn
x tan xsec x+tan x
sec x−1sec x+1