" 12."(tan x)^(log_(e)x)+(cos x)^(sin x)

Find the derivative of (tan x)^(log x)+(cos x)^(sin x) w.r.t.x.

int_( then p )^( If )(dx)/(1+tan x)=px+q log_(e)|cos x+sin x|+c

lim_(x rarr0)(sin x-log(e^(x)cos x))/(x sin x)

int(1)/(1+tan x)dx=(log)_(e)(x+sin x)+C(b)(log)_(e)(sin x+cos x)+C(c)2(sec^(2)x)/(2)+C(d)(1)/(2){x+log(sin x+cos x)}+C

cos^3x e^(log sin x)

If x in(0,(pi)/(2))-{1,(pi)/(4)} then the expression (log_(cos x)(x)*log_(tan x)(x))/(log_(cos x)(x)+log_(tan x)(x)) simplifies to

y = (tan x) / (x) log_ (e) ((e ^ (x)) / (x ^ (x)))

If y=(sin x)^(tan x), then (dy)/(dx)= (a) (sin x)^(tan x)(1+sec^(2)x log sin x)(b)tan x(sin x)^(tan x-1)cos x(c)(sin x)^(tan x)(d)sec^(2)x log sin x tan x(sin x)^(tan x-1)

lf_(log_(2)(3sin x)-log_(2)(cos x)-log_(2)(1-tan x)-log_(2)(1+tan x)=1) then tan x=