Natural Logarithm: Solutions

y = e^xlnx
$y' &sp;=&sp; e^x ln x^(ln x + x x) &sp;=&sp; e^x ln x^(ln x + 1)$
$h(x) &sp;=&sp; ln (e^x^ + 1) ln (e^x^ - 1)$
$dh dx &sp;=&sp; (e^x^e^x^ + 1) ln (e^x^ - 1) &sp;-&sp; (e^x^e^x^ - 1) ln (e^x^ + 1) ln^2^(e^x^
- 1)$
g(x) = log₁₀ (ln x)
$g '(x) &sp;=&sp; 1 x
(ln 10) (ln x)$
k(x) = ln (log₁₀ x)
$k '(x) &sp;=&sp; 1 x
(ln 10) (log_10_x) &sp;=&sp; 1 x ln x$
l(x) = (cos2x)^x = e^(x ln(cos2x))
$l '(x) &sp;=&sp;
(e^x ln (cos 2x)^) (ln (cos 2x) &sp;+&sp; (-2x sin 2x) cos 2x)$

jjnichol@mit.edu