Let `f(x+2y)=f(x)(f(y))^2` for all x,y and `f(0)=1.` If `f` is derivable at `x=0` then `f'(x)=`

Let f(x+y) = f(x) . f(y) for all x,y where f(0) ne 0. If f(5) =2 and f'(0) =3 , then f'(5) is equal to

Let f(x+y)+f(x-y)=2f(x)f(y) AA x,y in R and f(0)=k , then

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Range of y=log_(3//4)(f(x)) is

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Range of y=log_(3//4)(f(x)) is