Differenzialrechnung 1
Grundlagen, und Regeln der Differnezialrechnung
Grundlagen, und Regeln der Differnezialrechnung
Set of flashcards Details
| Flashcards | 23 |
|---|---|
| Language | Deutsch |
| Category | Maths |
| Level | Other |
| Created / Updated | 12.11.2016 / 20.05.2024 |
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\(\frac{d}{dx} \sin x\)
\(\frac{dx}{dy} \sin x = \cos x\)
\(\frac{d}{dx}\cot x\)
\(\frac{dx}{dy} \cot x = - \frac {1}{\sin^2 x} = -1 -\cot^2 x\)
\(\cos x\)
\(\frac{dx}{dy}\cos x = -\sin x\)
Ableitung von \(\tan x \)
\(\frac{dx}{dy} \tan x = \frac {1}{\cos^2 x} = 1 + \tan^2 x\)
Ableitung von ax
\((\ln a) \cdot a^x\)
Ableitung von ln x
\(\frac{1}{x}\)
Ableitung von loga x
\(\frac{1}{(\ln a) \cdot x} \)
Ableitung sinh x
\(\frac{d}{dx}sinh \ x = cosh \ x\)
Ableitung cosh x
\(\frac{d}{dx} cosh \ x = sinh \ x\)
Ableitung tanh x
\(\frac{d}{dx} tanh \ x = \frac{1}{cosh^2 \ x} = 1-tanh^2 \ x \)
Ableitung coth x
\(\frac{d}{dx} coth \ x= -\frac{1}{sinh^2 \ x} = 1-coth^2 \ x \)
Ableitung von xn
\(\frac{d}{dx} x^n = n \cdot x^{n-1}\)
Ableitung von e-x
\(\frac{d}{dx} e^{-x}=-e^{-x}\)
Ableitung von eax
\( \frac{d}{dx} e^{ax}=ae^{ax}\)
Ableitung von sin(ax + b)
\(\frac{d}{dx} sin(ax + b)=a \cdot cos(ax + b)\)
Ableitung von cos(ax + b)
\(\frac{d}{dx} \ cos(ax + b)= -a \cdot sin(ax+b)\)
Ableitung von tan(ax + b)
\(\frac{d}{dx} tan(ax+b)= a \ sec^2(ax+b)\)
Ableitung von cot(ax + b)
\(\frac{d}{dx} cot(ax + b)=-a \cdot cosec^2(ax+b)\)
Ableitung von sin-1(ax + b)
\(\frac{d}{dx} sin^{-1}(ax + b) = \frac{a}{\sqrt{1-(ax+b)^2}} \)
\(x^{-2} =\)
\(\frac{1}{x^2}\)
\(\sqrt[3]{x^5} =\)
\(x^{\frac{5}{3}} \)
\(\frac{dy}{dx} \sqrt{x}\)
\(= x^{-\frac{1}{2}} = \frac{1}{2} \cdot x^{- \frac{1}{2}} = \frac{1}{2 \cdot \sqrt{x}}\)
\(\frac{d}{dx}-x\)
\(-1\)
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