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

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

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

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

Let f(x) be a function satisfying f(x+y)=f(x)f(y) for all x,y in R and f(x)=1+xg(x) where underset(x to 0)lim g(x)=1 . Then f'(x) is equal to

If f(x)=log_(e)x and g(x)=e^(x) , then prove that : f(g(x)}=g{f(x)}

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

A function f : R to R Satisfies the following conditions (i) f (x) ne 0 AA x in R (ii) f(x +y)= f(x) f(y) AA x, y, in R (iii) f(x) is differentiable (iv ) f'(0) =2 The derivative of f(x) satisfies the equation