If `f: R^+vecR ,f(x)+3xf(1/x)=2(x+1),t h e nfin df(x)dot`

If f: RvecR is an odd function such that f(1+x)=1+f(x) and x^2f(1/x)=f(x),x!=0 then find f(x)dot

If f(x) is a polynomial function satisfying f(x)dotf(1/x)=f(x)+f(1/x) and f(4)=65 ,t h e nfin df(6)dot

If f(x)=(f(x))/y+(f(y))/x holds for all real x and y greater than 0a n df(x) is a differentiable function for all x >0 such that f(e)=1/e ,t h e nfin df(x)dot

Consider f: R^(+)->R such that f(3)=1 for a in R^+ a n d """"f(x)dotf(y)+ f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot

If y=f(a^x)a n df^(prime)(sinx)=(log)_e x ,t h e nfin d(dy)/(dx), if it exists, where pi/2

Let f((x+y)/2)=(f(x)+f(y))/2fora l lr e a lxa n dy If f^(prime)(0) exists and equals -1a n df(0)=1,t h e n f i n d f(2)dot

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e nfin d(dy)/(dx)dot

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

Let f: R^+ ->R be a function which satisfies f(x)dotf(y)=f(x y)+2(1/x+1/y+1) for x , y > 0. Then find f(x)dot

A continuous function f(x)onRvec satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAA x ,y in RdotT h e n findf(x)dot