Notes in Integration und Differentiation

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Status	Last Update	Fields
Published	01/12/2025	\(f(x) = x^a\) \(f'\)?
Published	01/12/2025	\(f(x) = \sin(x)\)\(f'\)?
Published	01/12/2025	\(f(x) = \cos(x)\)\(f'\)?
Published	01/12/2025	\(f(x) = \ln(x)\)\(f'\)?
Published	01/12/2025	\(f(x) = \arcsin(x)\)\(f'\)?
Published	01/12/2025	\(f(x) = \arccos(x) +c\)\(f'(x)=?\)
Published	01/12/2025	\(f(x) = a\)\(f'\) nach \(dx\)
Published	01/12/2025	\(f(x) = a \cdot x\)\(f'\)?
Published	01/12/2025	\(f(x) = e^x\)\(f'\)?
Published	01/12/2025	\(f(x) = a^x\)\(f'\)?
Published	01/12/2025	Sei \(f\) die Komposition \((v \circ u)\).\(f' ?\)
Published	01/12/2025	Sei \(f = u \cdot v\) \(f'=?\)
Published	01/12/2025	Sei \(f= \frac{u}{v}\)\(f'=?\)
Published	01/12/2025	\((a f)' =\)
Published	01/12/2025	\((f+g)' =\)
Published	01/12/2025	\(\frac{df^{-1}}{dx} =\) mit bekanntem \(f'\)
Published	01/12/2025	Ableitung \(y '\) nach \(x\)mit \(x = x(t), y = y(t)\) in Parameter Form:
Published	01/12/2025	Satz von Schwartz
Published	01/12/2025	\(f(x)=\tan(x)\)\(f'(x)=?\)
Published	01/12/2025	\(\sin(x), \,\cos(x) \:in \: \: \mathbb{C}\)
Published	01/12/2025	\[f(x)=\ln(g(x)) +c\]\[f'(x)=\ ?\]
Published	01/12/2025	Steigung einer impliziten Funktion mit \(F(x,y) = 0\)
Published	01/12/2025	\(f(x) = \arctan(x) +c\)\(f'(x) = ?\)
Published	01/12/2025	\(f(x) = \text{arccot} (x)\)\(f'(x) = ?\)
Published	01/12/2025	\(f(x)=A\)\(F(x)=?\)
Published	01/12/2025	\(f(x) = x^a\)\(F(x) ?\)
Published	01/12/2025	\(f(x) = e^x\)\(F(x)?\)
Published	01/12/2025	\(f(x) = e^{ax}\)\(F(x)?\)
Published	01/12/2025	\(f(x) = \frac{1}{\alpha x + \beta}\)\(F(x)?\)
Published	01/12/2025	\(f(x) = a^x\)\(F(x)?\)
Published	01/12/2025	\(f(x) = \sin(x)\)\(F(x)?\)
Published	01/12/2025	\(f(x) = \cos(x)\)\(F(x)?\)
Published	01/12/2025	\(f(x) = \sinh(x)\)\(F(x)?\)
Published	01/12/2025	\(f(x) = \cosh(x)\)\(F(x)?\)
Published	01/12/2025	Volumen eines Drehkörpers um die x-Achse mit Radius \(f(x)\) von Höhe \(a\) bis Höhe \(b\)
Published	01/12/2025	Bogenlänge \(s\) des Funktionsgraphen von \(f(x)\)
Published	01/12/2025	Gesamtbogenlänge \(s'\)des Graphen einer Funktion in Parameter Form mit\(x = x(t)\)\(y=y(t)\)mit den Grenzen \(t=\alpha\)\(t=\beta\)
Published	01/12/2025	\((x^x)'\)
Published	01/12/2025	\(f(x) = \ln\|x\|\)\(F(x) ?\)
Published	01/12/2025	Mittelwert der Funktion \(f(t)\) in den Grenzen \(a, b\)
Published	01/12/2025	\(f(x) = \sqrt{x}\)\(f' ?\)
Published	01/12/2025	Welche Körper entstehen beikonstanten Kugelkoordinaten?\(r, \vartheta, \varphi = const\)
Published	01/12/2025	Doppelintegral:KoordinatentransformationKartesisch auf Polar(grenzen)\(f(x,y) \rightarrow\)\(dA \rightarrow\)
Published	01/12/2025	Dreifach Integral: Koord. TransformationKartesisch \(\rightarrow\) Zylinder, Kugel 1. \(f(x,y,z) \rightarrow\)2. \(dV = dx dy dz \rightarrow \)3. Gren…
Published	01/12/2025	Volumen eines Zylinders mit \({\int \int \int}_{V_z}\)
Published	01/12/2025	Wie geht man bei der Partialbruchzerlegung vor?
Published	01/12/2025	\(a^x :=\)mit \(\exp\)
Published	01/12/2025	\(\frac{\log_b(x)}{\log_b(a)} =\)
Published	01/12/2025	\(\ln(a^x) =\)
Published	01/12/2025	\(\int \cos^2 (x) dx =\)
Published	01/12/2025	\(\int \frac{1}{1+x^2} dx =\)
Published	01/12/2025	\(\int \cos(d \cdot x) dx\)
Published	01/12/2025	\(\int \sin^2(x)\,dx\)
Published	01/12/2025	\(\cos(2x) =\) (mit Additionstheorem für \(\cos(x+y)\))
Published	01/12/2025	\(\int \sin(2x) =\)
Published	01/12/2025	\(\int_a^b \sin(x) \cos(x) \; dx=\)
Published	01/12/2025	\(\int_a^b \cos^2(x) \cdot \sin(x) \; dx =\)
Published	01/12/2025	\(f(x)=\int \frac{1}{\sqrt{1-x^2}} dx\)\(f(x)=?\)
Published	01/12/2025	\(\int \frac{-1}{\sqrt{1-x^2}} dx\)
Published	01/12/2025	\(\int \frac{1}{\sqrt{x}} dx\)
Published	01/12/2025	Funktionaldeterminante: Polarkoordinatensystem
Published	01/12/2025	Funktionaldeterminante: Zylinderkoordinatensystem
Published	01/12/2025	Funktionaldeterminante: Kugelkoordinatensystem
Published	01/12/2025	\(\cos(2x)=\)(mit \(\cos^2\))
Published	01/12/2025	\(f(x)= \text{arcoth} (x)\)\(f(x)=\text{artanh}(x)\)\(f'(x) =?\)
Published	01/12/2025	Def. Gradient
Published	01/12/2025	Definition Richtungsableitung Sei \(V(x,y,z)\) eine skalare Funktion und man möchte die Ableitung in Richtung \(\vec{e}_a=\frac{\v…
Published	01/12/2025	Definiton Divergenz \(\text{div}\)mathematisch
Published	01/12/2025	Definition Laplace-Operator (Skalar- und Vektorfeld)
Published	01/12/2025	Wie integriert man inverse trigonometrische Funktionen? (Beispiel \(\arctan(x)\))
Published	01/12/2025	\(f'(x)=\frac{1}{\sin^2(x)}\)\(f(x)=?\)
Published	01/12/2025	Für Integration (Nenner): You see:\(\sqrt{x^2+a^2}\)
Published	01/12/2025	\[\frac{df(u)}{du}=\frac{1}{\sqrt{a^2-u^2}}\]\(f(u)=?\)
Published	01/12/2025	POV: Du löst eines der beiden bestimmten Integrale \[\int \sin^2(x)\ dx, \; \int \cos ^2(x) \ dx\]mit den Grenzen \(0,\pi\) oder \…
Published	01/12/2025	\(\frac d {du} f(u)=\frac{1}{u^2} \)\(f(u)=?\)
Published	01/12/2025	\(\frac{e^x}{x^k} \xrightarrow{x\to\infty}\)mit \(k \in \mathbb{N}_0\)
Published	01/12/2025	\(\frac{x^k}{e^x} \xrightarrow{x\to\infty}\)\(k\in\mathbb N_0\)
Published	01/12/2025	\(\frac{\ln(x)}{x^k} \xrightarrow{x\to\infty}\)\(k\in\mathbb N\backslash\set{0}\)
Status	Last Update	Fields