# Ecercici 07.3

## apartat a)

kill(all)$

f(x):=cos( x + 1/(log(x^2 + 2)) );

diff(f(x), x);

ratsimp(%);

## apartat b)

kill(all)$

f(x):=atan(log(x)) + log(atan(x));

diff(f(x), x);

ratsimp(%);

factor(%);

## apartat c)

kill(all)$

f(x):=(sqrt(cos(x))) * (a^(sqrt(cos(x))));

diff(f(x), x);

ratsimp(%);

factor(%);

## apartat d)

kill(all)$

f(x):=atan( sqrt((1-cos(x))/(1+cos(x))) );

diff(f(x), x);

ratsimp(%);

## apartat e)

kill(all)$

f(x):= log ( (sqrt(1+x) + sqrt(1-x)) / (sqrt(1+x) - sqrt(1-x)));

diff(f(x), x);

ratsimp(%);

factor(%);

## apartat f)

kill(all)$

f(x):= sqrt( x + sqrt( x + sqrt( x + sqrt (x)) ) );

diff(f(x), x);

ratsimp(%);