Notes in Integrale und Ableitungen

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Status	Last Update	Fields
Published	11/22/2023	\(f(x) = x^a\) \(f'\)?
Published	11/22/2023	\(f(x) = x\), \(f'\)?
Published	11/22/2023	\(f(x) = sin(x)\)\(f'\)?
Published	11/22/2023	\(f(x) = cos(x)\)\(f'\)?
Published	11/22/2023	\(f(x) = ln(x)\)\(f'\)?
Published	11/22/2023	\(f(x) = arcsin(x)\)\(f'\)?
Published	11/22/2023	\(f(x) = \arccos(x)\)\(f'\)?
Published	11/22/2023	\(f(x) = a\)\(f'\) nach \(dx\)
Published	11/22/2023	\(f(x) = a \cdot x\)\(f'\)?
Published	11/22/2023	\(f(x) = e^x\)\(f'\)?
Published	11/22/2023	\(f(x) = a^x\)\(f'\)?
Published	11/22/2023	Sei \(f\) die Komposition \((v \circ u)\).\(f' ?\)
Published	11/22/2023	Sei \(f = u \cdot v\) \(f'=?\)
Published	11/22/2023	Sei \(f= \frac{u}{v}\)\(f'=?\)
Published	11/22/2023	\((a f)' =\)
Published	11/22/2023	\((f+g)' =\)
Published	11/22/2023	\(\frac{df^{-1}}{dx} =\) mit bekanntem \(f'\)
Published	11/22/2023	Ableitung \(y '\) nach \(x\)mit \(x = x(t), y = y(t)\) in Parameter Form:
Published	11/22/2023	Satz von Schwartz
Published	11/22/2023	\(\tan(x)' =\)
Published	11/22/2023	Steigung einer impliziten Funktion mit \(F(x,y) = 0\)
Published	11/22/2023	\(f(x) = \arctan(x)\)\(f' = ?\)
Published	11/22/2023	\(f(x) = arccot (x)\)\(f' = ?\)
Published	11/22/2023	\(f(x)=A\)\(F(x)=?\)
Published	11/22/2023	\(f(x) = x^a\)\(F(x) ?\)
Published	11/22/2023	\(f(x) = e^x\)\(F(x)?\)
Published	11/22/2023	\(f(x) = e^{ax}\)\(F(x)?\)
Published	11/22/2023	\(f(x) = \frac{1}{\alpha x + \beta}\)\(F(x)?\)
Published	11/22/2023	\(f(x) = a^x\)\(F(x)?\)
Published	11/22/2023	\(f(x) = sin(x)\)\(F(x)?\)
Published	11/22/2023	\(f(x) = cos(x)\)\(F(x)?\)
Published	11/22/2023	\(f(x) = sinh(x)\)\(F(x)?\)
Published	11/22/2023	\(f(x) = cosh(x)\)\(F(x)?\)
Published	11/22/2023	Partielle Integration (Produktregel)
Published	11/22/2023	Volumen eines Drehkörpers um die x-Achse mit Radius \(f(x)\) von Höhe \(a\) bis Höhe \(b\)
Published	11/22/2023	Bogenlänge \(s\) des Funktionsgraphen von \(f(x)\)
Published	11/22/2023	Gesamtbogenlänge \(s'\)des Graphen einer Funktion in Parameter Form mit\(x = x(t)\)\(y=y(t)\)mit den Grenzen \(t=\alpha\)\(t=\beta\)
Published	11/22/2023	\((x^x)'\)
Published	11/22/2023	\(\int \, \ln(x) \, dx\)
Published	11/22/2023	\(f(x) = ln(x)\)\(F(x) ?\)
Published	11/22/2023	Mittelwert der Funktion \(f(t)\) in den Grenzen \(a, b\)
Published	11/22/2023	\(f(x) = \sqrt{x}\)\(f' ?\)
Published	11/22/2023	\( \int \frac{1}{x^2 + a^2} dx \)
Published	11/22/2023	\(\int \frac{1}{\sqrt{1-x^2}} dx\)
Published	11/22/2023	\(\int \frac{-1}{\sqrt{1-x^2}} dx\)
Published	11/22/2023	\(f(x) = \arctan(x) +c\) \(f'(x) = ? \)
Published	11/22/2023	\( f(x)= arccot(x) +c,\ \int f'(x)dx=-\arctan(x)+c\)\(f'(x) = ? \)
Published	11/22/2023	\( f(x) = \frac{1}{\alpha x + \beta}+c\)\(f'(x)=?\)
Published	11/22/2023	\(\int \frac{1}{\sqrt{x}} dx\)
Published	11/22/2023	\(f'(x)=\tanh(x) \) \( f(x)=?\)
Published	11/22/2023	\(f(x)=\tanh(x) +c \)\(f'(x)=? \)
Published	11/22/2023	\( f(x)=\coth(x) +c\)\(f'(x)=?\)
Published	11/22/2023	\(f(x)=\frac{1}{2}\cdot \left( x+\sin(x)\cos(x)\right)+c\)\(f'(x)=? \)
Published	11/22/2023	\(f(x)=\frac{1}{2}\cdot \left( x-\sin(x)\cos(x)\right) +c\)\(f'(x)=? \)
Published	11/22/2023	\(f(x)= \frac{1}{2}\cdot \left(\sinh(x)\cosh(x) +x\right)\)\(f'(x)=?\)
Published	11/22/2023	\(f(x)= \frac{1}{2}\cdot \left(\sinh(x)\cosh(x) -x\right)+c\)\(f'(x)=? \)
Published	11/22/2023	\(\int \sqrt{a^2-x^2} dx \)
Published	11/22/2023	Funktionaldeterminante: Polarkoordinatensystem
Published	11/22/2023	Funktionaldeterminante: Zylinderkoordinatensystem
Published	11/22/2023	Funktionaldeterminante: Kugelkoordinatensystem
Published	11/22/2023	(grobe) Partialbruchzerlegung von:\(f(x)=\frac{x^2}{(x-1)^2(x-2)} \)
Published	11/22/2023	\(\int \frac{1}{x^2+a^2}dx\)
Published	11/22/2023	\(\int \frac{1}{x^2-a^2} dx\)
Published	11/22/2023	Welche Körper entstehen beikonstanten Kugelkoordinaten?\(r, \vartheta, \varphi = const\)
Published	11/22/2023	Doppelintegral:KoordinatentransformationKartesisch auf Polar(grenzen)\(f(x,y) \rightarrow\)\(dA \rightarrow\)
Published	11/22/2023	Dreifach Integral: Koord. TransformationKartesisch \(\rightarrow\) Zylinder, Kugel 1. \(f(x,y,z) \rightarrow\)2. \(dV = dx dy dz \rightarrow \)3. Gren…
Published	11/22/2023	Volumen eines Zylinders mit \({\int \int \int}_{V_z}\)
Published	11/22/2023	Wie geht man bei der Partialbruchzerlegung vor?
Published	11/22/2023	\(\sin(x) \:in \: \: \mathbb{C}\)
Published	11/22/2023	\(a^x :=\)mit \(\exp\)
Published	11/22/2023	\(\frac{\log_b(x)}{\log_b(a)} =\)
Published	11/22/2023	\(\ln(a^x) =\)
Published	11/22/2023	\(\sqrt[q]{a^p}\)
Published	11/22/2023	Sei \(a > 0\)\(\lim_{n \rightarrow \infty} \;\:\sqrt[n]{a} =\)
Published	11/22/2023	\(\frac{e^x}{x^k} \rightarrow\)mit \(k \in \mathbb{N}\)
Published	11/22/2023	\(\frac{x^k}{e^x} \rightarrow\)
Published	11/22/2023	\(\frac{\ln(x)}{x^k} \rightarrow\)
Published	11/22/2023	\(Sei \;7 = 10^x\) \(x=\)
Published	11/22/2023	\(\cos(2x)=\)
Published	11/22/2023	\(\int \cos^2 (x) dx =\)
Published	11/22/2023	\(\int \frac{1}{1+x^2} dx =\)
Published	11/22/2023	\(\int_{a}^{b} \sqrt{1-x^2} dx =\)Substituiere!
Published	11/22/2023	\(\int_{a}^{b}\sqrt{a-x^2}dx\)Substituiere!
Published	11/22/2023	\(\int \cos(d \cdot x) dx\)
Published	11/22/2023	\(\int \sin^2(x)\,dx\)
Published	11/22/2023	\(\cos(2x) =\)
Published	11/22/2023	\(\int \sin(2x) =\)
Published	11/22/2023	\(\int \cot(x) dx\)
Published	11/22/2023	\(\int_{a}^{b} \sqrt{c - x^2} \;dx =\)Substituiere!
Published	11/22/2023	\(\int_a^b \sin(x) \cos(x) \; dx=\)
Published	11/22/2023	\(\int_a^b \cos^2(x) \cdot \sin(x) \; dx =\)
New Card	11/23/2023	\(\int \frac{1}{1-x^2}dx \)
New Card	11/23/2023	\(\frac{\partial}{\partial x}\left(arcoth(x) \right) =?\)
New Card	11/23/2023	\(\int \frac{1}{\sqrt{x^2+1}}dx\)
New Card	11/23/2023	\(\int \frac{1}{\sqrt{x^2-1}}dx \)
New Card	11/23/2023	\(f(x) = sin^2(x)\)\(f'(x)=?\)
New Card	11/23/2023	\(f(x)=cos^2(x)\)\(f'(x)=?\)
New Card	11/23/2023	\(f'(x) = cos(2x)\)\(f(x)=?\)
New Card	11/23/2023	\(\int \frac{1}{x^3} dx \)
New Card	11/23/2023	\(\int \frac{1}{u^2} du \)
New Card	11/23/2023	\(z \cdot \bar z =?\)\((Re(z) = a, \; Im(z) =b)\)
Status	Last Update	Fields