A$\mathrm{.}1)(20$ minutes$)$

Let a$,$ x in IR$,$ a $0.$ Calculate the derivative of

$444434444214444434444421)$x$($h:

$223$

$)$x$($g:

$22$

$22$

$3$ xa

$2$xa

arctan

$2$a$2$

$1$

a$2$xax

a$2$xax

ln

$2$a$4$

$1$

$)$x$($f

$==$

$$

$$

$$

$$

$$

$$

$$

$+$

$$

$$

$$

$$

$$

$+$

$++$

$=$

and simplify as far as possible. Hint: The final expression is surprisingly simple.

Approximately half of the points are for simplifying. Differentiate and simplify g$($x$)$ and

h$($x$)$ separate as far as possible. ln means the natural logarithm.