`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

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

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

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)]

The value of (d)/(dx)5^(f(x)) 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. (a) Statement 1 and Statement 2, both are correct. Statement 2 is the correct explanation for Statement 1 (b) Statement 1 and Statement 2, both are correct. Statement 2 is not the correct explanation for Statement 1 (c) Statement 1 is correct but Statement 2 is not correct. (d) Both Statement 1 and Statement 2 are not correct.

If f (x) = tan ^(-1) ((cos x- sinx)/(cos x+ sin x)) then the value of (d)/(dx) f(x) is-

If f(x) 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 , then the value of n is

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(x)=(3)/(4)x+1,f^(n)(x) be defined as f^(2)(x)=f(f(x)), and for n ge 2, f^(n+1)(x)=f(f^(n)(x))." If " lambda =underset (n to oo)(lim)f^(n)(x), then show that λ is independant of x.

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .