Let `f(x+y)=f(x)+f(y)+2x y-1` for all real `xa n dy` and `f(x)` be a differentiable function. If `f^(prime)(0)=cosalpha,` the prove that `f(x)>0AAx in Rdot`

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

If f(x+y)=f(x)dotf(y),\ AAx in R\ a n df(x) is a differentiability function everywhere. Find f(x) .

f(x+y)=f(x).f(y)AA x,y in R and f(x) is a differentiable function and f'(0)=1,f(x)!=0 for any x.Findf(x)

A function f:R rarr R satisfies the equation f(x+y)=f(x)f(y) for allx,y in R and f(x)!=0 for all x in R .If f(x) is differentiable at x=0 .If f(x)=2, then prove that f'(x)=2f(x) .

If f(x+y)=f(x).f(y) for all real x,y and f(0)!=0, then the function g(x)=(f(x))/(1+{f(x)}^(2)) is:

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 real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)