`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 inN 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

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

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

Let f_(1)(x)=e^(x),f_(2)(x)=e^(f_(1)(x)),......,f_(n+1)(x)=e^(f_(n)(x)) for all n>=1. Then for any fixed n,(d)/(dx)f_(n)(x) is

Let f_1(x)=e^x,f_2(x)=e^(f_1(x)),"........",f_(n+1)(x)=e^(f_n(x)) for all nge1 . Then for any fixed n,(d)/(dx)f_n(x) is

f(x)=e^(-(1)/(x)), where x>0, Let for each positive integer n,P_(n) be the polynomial such that (d^(n)f(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)]

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

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