Let `f(x+y) = f(x) f(y) and f(x) = 1 + x g(x) G(x)` where `lim_(x->0) g(x) =a and lim_(x->o) G(x) = b. `Then `f'(x)` is

If f(x+y)=f(x)f(y) and f(x)=1+"xg(x) G(x)" , where lim_(xto0)g(x)=a and lim_(xto0)" G(x)=b . Then f'(x) is equal to :

Let f(x+y)=f(x)f(y) and f(x)=1+xg(x)G(x) where lim_(x rarr0)g(x)=a and lim_(x rarr o)G(x)=b Then f'(x) is

Let f(x+y)=f(x)f(y)andf(x)=1+xg(x)phi(x)" where "lim_(x to 0) g(x)=a andlim_(x to 0) phi(x)=b . Then what is f(x) equal to?

Let f(x+y)=f(x)f(y) and where f(x)=1+xg(x)phi(x) , lim_(xto0)g(x)=a and lim_(xto0)phi(x)=b Then what is f'(x) equal to ?

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

Let f(x+y)=f(x)f(y) and f(x) = 1 + (sin2x) g(x) where g(x) is continuous . Then f^(1) (x) equals

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.