Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): `f(x)=(|sinx+cosx|)/(|sinx|+|cosx|)`

Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): f(x)=tanpi/2[x]

Find the period (if periodic) of the following function ([.] denotes the greatest integer functions): f(x)=x-[x-b],b in R

Find the derivative of the following function f(x) = x-3 sinx

Find the period (if periodic) of the following function f(x)=e^(log(sinx))+tan^3x-cos e c(3x-5)

Integrate the functions e^(x)(sinx+cosx)dx

Find the domain of the following functions f(x)=sin^(-1)x+cosx

Find the period of the following. (i) f(x)=(2^(x))/(2^([x])) , where [.] represents the greatest integer function. (ii) f(x)=e^(sinx) (iii) f(x)=sin^(-1)(sin 3x) (iv) f(x) =sqrt(sinx) (v) f(x)=tan((pi)/(2)[x]), where [.] represents greatest integer function.

Integrate the functions (sinx)/(1+cosx)

Integrate the functions e^(x)((1+sinx)/(1+cosx))

Find the period of the following function (i) f(x) =|sinx|+|cosx| (ii) f(x)=cos(cosx)+cos(sinx) (iii) f(x)= (|sinx+cosx|)/(|sinx|+|cosx|)