Предмет: Алгебра,
автор: budiakanastas11
Найти значение выражения:
(две тритих + семь восьмых - пять шестых) * (один - пять седьмых)
Найти первую и вторую производные:
у=3x^4 - x^2 +x (в степени "дробь" минус две третьих) +12
Выполнить умножение:
(2a-1)^2 * (1+2a+4a^2)
Ответы
Автор ответа:
0
1) ![( frac{2}{3}+ frac{7}{8}- frac{5}{6})*(1- frac{5}{7})= frac{2*8+7*3-5*4}{24}* frac{7-5}{7} = frac{18+21-20}{24}* frac{2}{5} = frac{19}{24}* frac{2}{5}= ( frac{2}{3}+ frac{7}{8}- frac{5}{6})*(1- frac{5}{7})= frac{2*8+7*3-5*4}{24}* frac{7-5}{7} = frac{18+21-20}{24}* frac{2}{5} = frac{19}{24}* frac{2}{5}=](https://tex.z-dn.net/?f=%28+frac%7B2%7D%7B3%7D%2B+frac%7B7%7D%7B8%7D-+frac%7B5%7D%7B6%7D%29%2A%281-+frac%7B5%7D%7B7%7D%29%3D+frac%7B2%2A8%2B7%2A3-5%2A4%7D%7B24%7D%2A+frac%7B7-5%7D%7B7%7D+%3D+frac%7B18%2B21-20%7D%7B24%7D%2A+frac%7B2%7D%7B5%7D+%3D+frac%7B19%7D%7B24%7D%2A+frac%7B2%7D%7B5%7D%3D++++)
![frac{19}{2*5}= frac{19}{10}=1 frac{9}{10} frac{19}{2*5}= frac{19}{10}=1 frac{9}{10}](https://tex.z-dn.net/?f=+frac%7B19%7D%7B2%2A5%7D%3D+frac%7B19%7D%7B10%7D%3D1+frac%7B9%7D%7B10%7D++)
2)![frac{d}{dx}(3x^4-x^2+ x^{- frac{2}{3}}+12)= frac{d}{dx}(12)- frac{d}{dx}(x^2)+3( frac{d}{dx}(x^4) )- frac{d}{dx}( x^{- frac{2}{3} } )= frac{d}{dx}(3x^4-x^2+ x^{- frac{2}{3}}+12)= frac{d}{dx}(12)- frac{d}{dx}(x^2)+3( frac{d}{dx}(x^4) )- frac{d}{dx}( x^{- frac{2}{3} } )=](https://tex.z-dn.net/?f=+frac%7Bd%7D%7Bdx%7D%283x%5E4-x%5E2%2B+x%5E%7B-+frac%7B2%7D%7B3%7D%7D%2B12%29%3D+frac%7Bd%7D%7Bdx%7D%2812%29-+frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3%28+frac%7Bd%7D%7Bdx%7D%28x%5E4%29+%29-+frac%7Bd%7D%7Bdx%7D%28+x%5E%7B-+frac%7B2%7D%7B3%7D+%7D+%29%3D++++)
![-( frac{d}{dx}( x^{- frac{2}{3} } ) )- frac{d}{dx}(x^2)+3( frac{d}{dx}(x^4) )+0= - frac{-2}{3 x^{ frac{5}{3} } }-2x+3*4x^3= -( frac{d}{dx}( x^{- frac{2}{3} } ) )- frac{d}{dx}(x^2)+3( frac{d}{dx}(x^4) )+0= - frac{-2}{3 x^{ frac{5}{3} } }-2x+3*4x^3=](https://tex.z-dn.net/?f=-%28+frac%7Bd%7D%7Bdx%7D%28+x%5E%7B-+frac%7B2%7D%7B3%7D+%7D+%29+%29-+frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3%28+frac%7Bd%7D%7Bdx%7D%28x%5E4%29+%29%2B0%3D+-+frac%7B-2%7D%7B3+x%5E%7B+frac%7B5%7D%7B3%7D+%7D+%7D-2x%2B3%2A4x%5E3%3D+++)
![frac{2}{3 x^{ frac{5}{3} } }-2x+12x^3 frac{2}{3 x^{ frac{5}{3} } }-2x+12x^3](https://tex.z-dn.net/?f=frac%7B2%7D%7B3+x%5E%7B+frac%7B5%7D%7B3%7D+%7D+%7D-2x%2B12x%5E3)
![frac{ d^{2} }{dx^2}(3x^4-x^2- x^{ -frac{2}{3}}+12)= frac{d}{dx}(frac{d}{dx}(3x^4-x^2- x^{ -frac{2}{3}}+12))= frac{ d^{2} }{dx^2}(3x^4-x^2- x^{ -frac{2}{3}}+12)= frac{d}{dx}(frac{d}{dx}(3x^4-x^2- x^{ -frac{2}{3}}+12))=](https://tex.z-dn.net/?f=+frac%7B+d%5E%7B2%7D+%7D%7Bdx%5E2%7D%283x%5E4-x%5E2-+x%5E%7B+-frac%7B2%7D%7B3%7D%7D%2B12%29%3D+frac%7Bd%7D%7Bdx%7D%28frac%7Bd%7D%7Bdx%7D%283x%5E4-x%5E2-+x%5E%7B+-frac%7B2%7D%7B3%7D%7D%2B12%29%29%3D)
![frac{d}{dx}( frac{d}{dx}(12)-frac{d}{dx}( x^{- frac{2}{3} })-frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))= frac{d}{dx}( frac{d}{dx}(12)-frac{d}{dx}( x^{- frac{2}{3} })-frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))=](https://tex.z-dn.net/?f=frac%7Bd%7D%7Bdx%7D%28+frac%7Bd%7D%7Bdx%7D%2812%29-frac%7Bd%7D%7Bdx%7D%28+x%5E%7B-+frac%7B2%7D%7B3%7D+%7D%29-frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3frac%7Bd%7D%7Bdx%7D%28x%5E4%29%29%3D)
![frac{d}{dx}(0-frac{d}{dx}( x^{- frac{2}{3} })-frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))=frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -frac{d}{dx}(x^2)+3frac{d}{dx}(x^4)) frac{d}{dx}(0-frac{d}{dx}( x^{- frac{2}{3} })-frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))=frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))](https://tex.z-dn.net/?f=frac%7Bd%7D%7Bdx%7D%280-frac%7Bd%7D%7Bdx%7D%28+x%5E%7B-+frac%7B2%7D%7B3%7D+%7D%29-frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3frac%7Bd%7D%7Bdx%7D%28x%5E4%29%29%3Dfrac%7Bd%7D%7Bdx%7D%280-+frac%7B-2%7D%7B3+x%5E%7B+frac%7B5%7D%7B3%7D+%7D+%7D+-frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3frac%7Bd%7D%7Bdx%7D%28x%5E4%29%29)
![=frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))=frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -2x+3*4x^3)= =frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -frac{d}{dx}(x^2)+3frac{d}{dx}(x^4))=frac{d}{dx}(0- frac{-2}{3 x^{ frac{5}{3} } } -2x+3*4x^3)=](https://tex.z-dn.net/?f=%3Dfrac%7Bd%7D%7Bdx%7D%280-+frac%7B-2%7D%7B3+x%5E%7B+frac%7B5%7D%7B3%7D+%7D+%7D+-frac%7Bd%7D%7Bdx%7D%28x%5E2%29%2B3frac%7Bd%7D%7Bdx%7D%28x%5E4%29%29%3Dfrac%7Bd%7D%7Bdx%7D%280-+frac%7B-2%7D%7B3+x%5E%7B+frac%7B5%7D%7B3%7D+%7D+%7D+-2x%2B3%2A4x%5E3%29%3D++)
![frac{2}{3}( frac{d}{dx}( x^{- frac{5}{3} } ) )-2( frac{d}{dx} (x))+12( frac{d}{dx}(x^3))= frac{2}{3}( frac{d}{dx}( x^{- frac{5}{3} } ) )-2( frac{d}{dx} (x))+12( frac{d}{dx}(x^3))=](https://tex.z-dn.net/?f=frac%7B2%7D%7B3%7D%28+frac%7Bd%7D%7Bdx%7D%28+x%5E%7B-+frac%7B5%7D%7B3%7D+%7D+%29+%29-2%28+frac%7Bd%7D%7Bdx%7D+%28x%29%29%2B12%28+frac%7Bd%7D%7Bdx%7D%28x%5E3%29%29%3D)
![-2( frac{d}{dx}(x))+12( frac{d}{dx}(x^3))+ frac{2}{3}* frac{-5}{3 x^{ frac{8}{3} } }=- frac{10}{9 x^{ frac{8}{3} } }-2*1+12*3x^2= -2( frac{d}{dx}(x))+12( frac{d}{dx}(x^3))+ frac{2}{3}* frac{-5}{3 x^{ frac{8}{3} } }=- frac{10}{9 x^{ frac{8}{3} } }-2*1+12*3x^2=](https://tex.z-dn.net/?f=-2%28+frac%7Bd%7D%7Bdx%7D%28x%29%29%2B12%28+frac%7Bd%7D%7Bdx%7D%28x%5E3%29%29%2B+frac%7B2%7D%7B3%7D%2A+frac%7B-5%7D%7B3+x%5E%7B+frac%7B8%7D%7B3%7D+%7D+%7D%3D-+frac%7B10%7D%7B9+x%5E%7B+frac%7B8%7D%7B3%7D+%7D+%7D-2%2A1%2B12%2A3x%5E2%3D++++)
![-2- frac{10}{9 x^{ frac{8}{3} } }+36x^2 -2- frac{10}{9 x^{ frac{8}{3} } }+36x^2](https://tex.z-dn.net/?f=-2-+frac%7B10%7D%7B9+x%5E%7B+frac%7B8%7D%7B3%7D+%7D+%7D%2B36x%5E2)
3)![(2a-1)^2 * (1+2a+4a^2)=(2a-1)^2*(2a+1)^2= (2a-1)^2 * (1+2a+4a^2)=(2a-1)^2*(2a+1)^2=](https://tex.z-dn.net/?f=%282a-1%29%5E2+%2A+%281%2B2a%2B4a%5E2%29%3D%282a-1%29%5E2%2A%282a%2B1%29%5E2%3D)
![(4a^2-4a+1)*(4a^2+4a+1)=16a^4+16a^3+4a^2-16a^3-16a^2-4a (4a^2-4a+1)*(4a^2+4a+1)=16a^4+16a^3+4a^2-16a^3-16a^2-4a](https://tex.z-dn.net/?f=%284a%5E2-4a%2B1%29%2A%284a%5E2%2B4a%2B1%29%3D16a%5E4%2B16a%5E3%2B4a%5E2-16a%5E3-16a%5E2-4a)
![+4a^2+4a+1=16a^4-8a^2+1 +4a^2+4a+1=16a^4-8a^2+1](https://tex.z-dn.net/?f=%2B4a%5E2%2B4a%2B1%3D16a%5E4-8a%5E2%2B1)
2)
3)
Похожие вопросы
Предмет: Математика,
автор: Аноним
Предмет: Қазақ тiлi,
автор: sara8515
Предмет: Математика,
автор: Аноним
Предмет: История,
автор: violettanefedova