`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

f_n(x)=e^(f_(n-1)(x)) for all n in Na n df_0(x)=x ,t h e n d/(dx){f_n(x)} is (a) (f_n(x)d)/(dx){f_(n-1)(x)} (b) f_n(x)f_(n-1)(x) (c) f_n(x)f_(n-1)(x).......f_2(x)dotf_1(x) (d)none of these

If f(x)=(x^2)/(|x|) , write d/(dx)(f(x))

Let f _(1)(x) =e ^(x) and f _(n+1) (x) =e ^(f _(n)(x))) for any n ge 1, n in N. Then for any fixed n, the vlaue of (d)/(dx) f )(n)(x) equals:

f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,P_n be the polynomial such that (d^nf(x))/(dx^n)=P_n(1/x)e^(-1/x) for all x > 0. Show that P_(n+1)(x)=x^2[P_n(x)-d/(dx)P_n(x)]

Le the be a real valued functions satisfying f(x+1) + f(x-1) = 2 f(x) for all x, y in R and f(0) = 0 , then for any n in N , f(n) =

f(x) = sin^(-1)(sin x) then (d)/(dx)f(x) at x = (7pi)/(2) is

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))_(x=a+4000)=b . Statement 2: f(x) is a periodic function with period 4.

If the function f: R-{(2005)/(153)}vecR-{(2005)/(153)} , defined by f(x)=(2005 x+153)/(153 x-2005) , then- (a) f^(-1)(x)=f(x) (b) f^(2014)(x)=x ,w h e r ef^n(x)=f(f(f(x)))n brackets (c)( f^(2013)(x)=x ,w h e r ef^n(x)=f(f(f(x)))n brackets (d) f^(-1)(x)=-f(x)

If d/dx (ϕ(x))=f(x) , then int_(1)^(2) f(x) dx is ______

If f(x)=x+1 , then write the value of d/(dx)(fof)(x) .