Mathematische Formelsammlung

11.2 Ableitungs- und Stammfunktionen F … Stammfunktion von f; k, q, C * R ; a * R +  \ {1} Funktion Ableitungsfunktion Stammfunktion y = f(x) = k y’ = f’(x) = 0 F(x) = ​ :  ​  ​ k​dx = kx + C y = f(x) = x q y’ = f’(x) = q · x q – 1 q ≠ ‒1: F(x) = ​ :  ​​ x q ​ dx = ​  x q + 1 _ q + 1  ​ + C q = ‒1, also f(x) = ​  1 _ x ​ : F(x) = ​ :  ​​ 1 _ x ​ dx = ln  ​ | x  | ​ + C y = f(x) = e x y’ = f’(x) = e x F(x) = ​ :  ​​ e x ​ dx = e x + C y = f(x) = a x y’ = f’(x) = a x  · lna F(x) = ​ :  ​​ a x ​ dx = ​  a x _  lna ​ + C y = f(x) = ln x y’ = f’(x) = ​  1 _ x ​ F(x) = ​ :  ​​ ln ​ x dx = x · ln x – x + C y = f(x) = a log x y’ = f’(x) = ​  1 _ x ​ ·  a loge = ​  1 _ x ​ ·  ​  1 _  lna ​ F(x) = ​ :  ​​ a ​ log x dx = = ​  1 _  lna ​ (x · ln x – x) + C y = f(x) = sin x y’ = f’(x) = cos x F(x) = ​ :  ​​ sin x ​ dx = ‒ cos x + C y = f(x) = cos x y’ = f’(x) = ‒ sin x F(x) = ​ :  ​​ cos x ​ dx = sinx + C y = f(x) = tan x y’ = f’(x) = ​  1 _  cos 2  x ​ = 1 + tan 2  x F(x) = ​ :  ​​ tan x ​ dx = ‒ ln  ​ | cos x  | ​ + C y = f(x) = cot x y’ = f’(x) = ​  ‒1 _  sin 2  x ​ = ‒ (1 + cot 2  x) F(x) = ​ :  ​​ cot x ​ dx = ln  ​ | sin x  | ​ + C Differential- und Integralrechnung 25 Nur zu Prüfzwecken – Eigentum des Verlags öbv