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

The equation x log x = 3 $$-$$ x

If $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to