If f(x+y)=f(x)f(y) for all x,y and f(x)=1+xg(x), where `underset(x to 0)lim g(x)=1`, show that, f'(x)=f(x).

If f(x+y)=f(x)f(y) for all x, y and f(x)=1+xg(x) , where lim_(xto0)g(x)=1 . Show that f'(x)=f(x) .

If f(x + y) = f(x)f(y) for all x, y and and f(x) = 1 + x g(x), where lim_(xrarr0)g(x)=1 ) , show that f'(x) = f(x).

If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) will be

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

If f(x + y) = f(x) - f(y), forall x, y in R , then show that f(3) = f(1)

The function f satisfies the relation f(x+y) =f(x) f(y) for all ral x, y and f(x) ne 0. If f(x) is differentiable at x=0 and f'(0) =2, then f'(x) is equal to-

If f(x+y+z)=f(x) f(y) f(z) ne 0 for all x,y,z and f(2)=5, f'(0)=2, find f'(2).

Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot