If `f(x-y)=f(x).g(y)-f(y).g(x)` and `g(x-y)=g(x).g(y)+f(x).f(y)` for all `x in R` . If right handed derivative at x=0 exists for f(x) find the derivative of g(x) at x =0

If f((x)/(y))=(f(x))/(f(y)) for all x, y in R, y ne 0 and f'(x) exists for all x, f(2) = 4. Then, f(5) is

If (f(x))^(g(y))=e^(f(x)-g(y)) then (dy)/(dx)=

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x, y in R and f(0)=0. Then,

Le f : R to R and g : R to R be functions satisfying f(x+y) = f(x) +f(y) +f(x)f(y) and f(x) = xg (x) for all x , y in R . If lim_(x to 0) g(x) = 1 , then which of the following statements is/are TRUE ?

Let f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x)AA x,y in R where g(x) is continuous then f'(x) is

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)