Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be

Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,

Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then

Let $${f_1}(x) = {e^x}$$, $${f_2}(x) = {e^{{f_1}(x)}}$$, ......, $${f_{n + 1}}(x) = {e^{{f_n}(x)}}$$ for all n $$ \ge $$ 1. Then for any fixed n, $${d \over {dx}}{f_n}(x)$$ is