restart;f := z -> exp(exp(exp(z)));

NiM+SSJmRzYiZio2I0kiekdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLUkkZXhwRzYkSSpwcm90ZWN0ZWRHRi9JKF9zeXNsaWJHRiU2Iy1GLTYjLUYtNiM5JEYlRiVGJQ==

f(x+I*y);

NiMtSSRleHBHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYjLUYkNiMtRiQ2IywmSSN4fGlyR0YoIiIiKiZeI0YwRjBJI3l8aXJHRihGMEYw

assume(x,real); assume(y,real); u := Re(f(x+I*y)); v := Im(f(x+I*y));

NiM+SSJ1RzYiKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGKkkoX3N5c2xpYkdGJTYjKiYtRig2IyomLUYoNiNJI3h8aXJHRiUiIiItSSRjb3NHRik2I0kjeXxpckdGJUY0RjQtRjY2IyomRjFGNC1JJHNpbkdGKUY3RjRGNEY0LUY2NiMqJkYuRjQtRj1GOkY0RjQ=NiM+SSJ2RzYiKiYtSSRleHBHNiRJKnByb3RlY3RlZEdGKkkoX3N5c2xpYkdGJTYjKiYtRig2IyomLUYoNiNJI3h8aXJHRiUiIiItSSRjb3NHRik2I0kjeXxpckdGJUY0RjQtRjY2IyomRjFGNC1JJHNpbkdGKUY3RjRGNEY0LUY9NiMqJkYuRjQtRj1GOkY0RjQ=

simplify(diff(u,x)-diff(v,y));

NiMiIiE=

simplify(diff(u,y)+diff(v,x));

NiMiIiE=Warning, done/quit/stop disabled. Please use File->Close

diff(f(z),z);

NiMqKC1JJGV4cEc2JEkqcHJvdGVjdGVkR0YnSShfc3lzbGliRzYiNiNJInpHRikiIiItRiU2I0YkRiwtRiU2I0YtRiw=