Kürzel und Tipps zu WolframAlpha

Kürzel und Tipps zu wolframalpha.com; wie ging noch der Befehl fürs Integriern, Ableiten, anderes?

• Ableiten
  
  sin(x^3+x+1)‘
  d/dy(d/dx sin(xy))
  table d^n/dx^n sin(xy) for n=1..4
• Integrieren
  integral xe^x
  integral(0,1) xe^x
  integral(1,8) 2/(yx^(1/3)) dx
  definite integral integral –x^2-y^2+4 dy dx over 0<=y<=1,0<=x<=2
• vereinfachen
  simplify 2x^2-7xy+3y^2
  factor 2x^2-7xy+3y^2
  factor 7654
  cancel ((x^3-1)/(x-1))
  apart (x^2+3x+4)/(x(x+1))
• Gleichungen, Ungleichungen
  solve x^2-3x+2=0
  Nullstellen roots x^2-3x+2
  solve 2x+3y=8,3x+4y=11
  solve 18<100/(19-x)+x<20 for integer x
  (Differenzialgleichung) solve x‘‘(t)-2x‘(t)+3x(t)=t+1,x(0)=1,x‘(0)=1
• Grenzwerte
  lim (x^n-1)/(x-1),x to 1
  lim (x^n-1)/(x-1),x->1
  lim (1+1/n)^n,n to infy
• Summe, Produkt
  sum k^2,k,1,n
  sum k^-2,k,1,infy
  product (k+2)/(k+1),k,0,n
• Taylorreihe: series e^x/sin(x),x=0
• Maximum, Minimum: max -x^3+3x+1 on -2<=x<=2
• Lineare Optimierung: max x+y on x<=12,y<=10,x+2y<=26,2x+y<=28
• Länge eines Vektors: norm{1,2,2}
• Matrixmultiplikation:
  {{1,2,3},{0,a,1}}.{{2},{1},{3}}
  {{1,2,3},{0,a,1}}.{{2,1},{b,3},{1,0}}
• Determinante: det{{12},{3,4}}
• Inverse: inverse{{1,2,3},{3,4,5},{a,0,0}}
• Eigenwerte: eigenvalue{{1,2,2},{2,2,1},{2,1,2}}