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

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 be function satisfying f(x+y)=f(x)+f(y) and f(x)=x^(2)g(x) , for all x and y, where g(x) is a continuous function. Then f'(x) is :

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) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,

Let f(x) be a function satisfying f(x+y)=f(x)+f(y) and f(x)=x g(x)"For all "x,y in R , where g(x) is continuous. Then,