`f_(n)(x)=e^(f_(n-1)(x))" for all "n in N and f_(0)(x)=x," then "(d)/(dx){f_(n)(x)}` is

If (d)/(dx)f(x)=cos x +sin x and f(0)=2 , then f(x)=.....

If f(x) satisfies the relation, f(x+y)=f(x)+f(y) for all x,y in R and f(1)=5, then find sum_(n=1)^(m)f(n) . Also, prove that f(x) is odd.

If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N such that f(1)=3 and sum_(x=1)^nf(x)=120 , find the value of n .

If f: N toN , f(x) = 2x +3 then …….

Let f be a function satisfying f(x+y)=f(x) + f(y) for all x,y in R . If f (1)= k then f(n), n in N is equal to

If d/(dx) (f(x))^(n)=n(f(x))^(n-1)(df(x))/(dx) then (d)/(dx) (sin^3x)=3sin^(2)x.cosx .

If f is a function satisfying f (x +y) = f(x) f(y) for all x, y in N such that f(1) = 3 and sum _(x=1)^nf(x)=120 , find the value of n.

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

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if ((d/(dx)f(x)))_(x=a)=b ,t h e n((d/(dx)f(x)))_(a+4000)=bdot Statement 2: f(x) is a periodic function with period 4.

Let f_1 (x,y)-=ax^2+2hxy+by^2=0 and let f_(i+1) (x,y)=0 denote the equation of the bisectors of f_i (x,y)=0 for all i=1,2,3,….. The value of sum_(n=2)^(5) (f_(n+2)(x,y))/(f_n(x,y)) is