`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 f(x) = 1 - x , find (d/dx)(fof)(x)

d/(dx)intf(x)dx=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.

Let f be a differentiable function satisfying [f(x)]^(n)=f(nx)" for all "x inR. Then, f'(x)f(nx) a. f(x) b. 0 c. f(x)f'(nx) d. none of these

Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and p(x),Q(x) be polynomial in x such that f(n+2)=P(n)f(n+1)+Q(n)f(n) for all n >= 1, Then (a) P(x) = x+3 (b) Q(x) = -x-2 (c) P(x) = -x-2 (d) Q(x) = x+3

d/(dx)(int f(x)dx)=

If d/(dx)(phi(x))=f(x) , then

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)^n f(x)=120 , find the value of n.

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 .