Differenzieren von Funktionen und Funktionstermen

Differenzieren von Funktionen:

>	f:= x -> 5*x^3 + x - 7; Df:= D(f); D2f:= D(Df);

>	f:= x -> a*x^n; Df:= x -> D(f)(x); Df(x):= simplify (D(f)(x)); Df(x):= sort (%);

Differenzieren von Funktionstermen:

>	f(x):= 5*x^3 + x - 7; Df(x):= diff (f(x), x); D2f(x):= diff (Df(x), x); diff (a, x);

Mehrmalige Differentiation einer Funktion f:

>	f:= sin; for i from 1 to 3 do    f||i:= (D@@i)(f) od;

Mehrmalige Differentiation eines Funktionsterms f(x) nach x:

>	restart; f(x):= sin(x); for i from 1 to 3 do    f||i(x):= diff(f(x),x$i) od;

Ableitungsregeln:

>	diff (a*u(x), x); # Faktorregel

>	diff (u(x)+v(x), x); # Summenregel

>	diff (u(x)*v(x), x); # Produktregel

>	simplify (diff (u(x)/v(x), x)); # Quotientenregel

>	diff (u(v(x)), x); # Kettenregel

Operatoren