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Einführung in Maple    
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Differenzieren

> restart;

Differenzieren von Funktionen:

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

f := proc (x) options operator, arrow; 5*x^3+x-7 end proc
Df := proc (x) options operator, arrow; 15*x^2+1 end proc 
D2f := proc (x) options operator, arrow; 30*x end proc 

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

f := proc (x) options operator, arrow; a*x^n end proc 
Df := proc (x) options operator, arrow; a*x^n*n/x end proc 
Df(x) := a*x^(n-1)*n 
Df(x) := n*a*x^(n-1) 

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); 

f(x) := 5*x^3+x-7
Df(x) := 15*x^2+1 
D2f(x) := 30*x

0

Mehrmalige Differentiation einer Funktion f:

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

f := sin
f1 := cos
f2 := -sin
f3 := -cos

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; 

f(x) := sin(x)
f1(x) := cos(x)
f2(x) := -sin(x)
f3(x) := -cos(x)

Ableitungsregeln:

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

a*diff(u(x),x)

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

diff(u(x),x)+diff(v(x),x)

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

diff(u(x),x)*v(x)+u(x)*diff(v(x),x)

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

(diff(u(x),x)*v(x)-u(x)*diff(v(x),x))/v(x)^2

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

D(u)(v(x))*diff(v(x),x)

Operatoren


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