1812256
Description
Flashcards by Leonard Euler, updated more than 1 year ago
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Created by Leonard Euler
almost 10 years ago
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| Question | Answer |
| \[\dfrac{d}{dx} c\] | \[0\] |
| \[\dfrac{d}{dx} x\] | \[1\] |
| \[\dfrac{d}{dx} x^2\] | \[2x\] |
| \[\dfrac{d}{dx} x^3\] | \[3x^2\] |
| \[\dfrac{d}{dx} x^k\] | \[k\cdot x^{k-1}\] |
| \[\dfrac{d}{dx} \dfrac{1}{x}\] | \[-\dfrac{1}{x^2}\] |
| \[\dfrac{d}{dx} \sqrt{x}\] | \[\dfrac{1}{2\sqrt{x}}\] |
| \[(\lambda\cdot u)'\] | \[\lambda\cdot u'\] |
| \[(u+v)'\] | \[u'+v'\] |
| \[(u\cdot v)'\] | \[u'\cdot v+u\cdot v'\] |
| \[\Big(\dfrac{1}{u}\Big)'\] | \[-\dfrac{u'}{u^2}\] |
| \[\Big(\dfrac{u}{v}\Big)'\] | \[\dfrac{u'\cdot v-u\cdot v'}{v^2}\] |
| \[(u\circ v)'\] | \[(u' \circ v)\cdot v'\] |
| \[(\sqrt{u})'\] | \[\dfrac{u'}{2\sqrt{u}}\] |
| \[(u^k)'\] | \[k\cdot u^{k-1}\cdot u'\] |
| \[\dfrac{d}{dx} \sin{x}\] | \[\cos{x}\] |
| \[\dfrac{d}{dx} \cos{x}\] | \[-\sin{x}\] |
| \[\dfrac{d}{dx} \tan{x}\] | \[1+\tan^2{x}=\dfrac{1}{\cos^2{x}}\] |
| \[(\sin{u})'\] | \[u'\cdot \cos{u}\] |
| \[(\cos{u})'\] | \[-u'\cdot \sin{u}\] |
| \[(\tan{u})'\] | \[u'\cdot(1+\tan^2{u})=\dfrac{u'}{\cos^2{u}}\] |
| \[\dfrac{d}{dx} e^x\] | \[e^x\] |
| \[\dfrac{d}{dx} \ln{x}\] | \[\dfrac{1}{x}\] |
| \[(e^u)'\] | \[u'\cdot e^u\] |
| \[(\ln{u})'\] | \[\dfrac{u'}{u}\] |
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