Differenzieren
> restart;
Differenzieren von Funktionen:
> f:= x -> 5*x^3 + x - 7;
Df:= D(f);
D2f:= D(Df);
D2f:= D(Df);
> f:= x -> a*x^n;
Df:= x -> D(f)(x);
Df(x):= simplify(D(f)(x));
Df(x):= sort(%);
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);
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;
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$i)
od;
for i from 1 to 3 do
f||i(x):= diff(f(x),x$i)
od;
> 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
