Сплавили два слитка золота с серебром. Масса первого слитка 4 кг, количество золота и серебра в нём находятся в отношении 1:7. М
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Только производные:
2.1
2.2
![y= \sqrt[3]{(4+3x)^2}=(4+3x)^{ \frac{2}{3} } \\ y'= \frac{2}{3}(4+3x)^{ \frac{2}{3}- \frac{3}{3} }*3=2(4+3x)^{- \frac{1}{3} }= \frac{2}{ \sqrt[3]{4+3x} }](https://tex.z-dn.net/?f=y%3D+%5Csqrt%5B3%5D%7B%284%2B3x%29%5E2%7D%3D%284%2B3x%29%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D+%5C%5C+%0Ay%27%3D+%5Cfrac%7B2%7D%7B3%7D%284%2B3x%29%5E%7B+%5Cfrac%7B2%7D%7B3%7D-+%5Cfrac%7B3%7D%7B3%7D++%7D%2A3%3D2%284%2B3x%29%5E%7B-+%5Cfrac%7B1%7D%7B3%7D+%7D%3D+%5Cfrac%7B2%7D%7B+%5Csqrt%5B3%5D%7B4%2B3x%7D+%7D+++)
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![y= \sqrt[4]{1+cos^{2}x} =(1+cos^{2}x)^{ \frac{1}{4} } \\ y'= \frac{1}{4}(1+cos^2x)^{ \frac{1}{4}- \frac{4}{4} }*(2cosx*(-sinx))= \\ = \frac{1}{4}(1+cos^2x)^{- \frac{3}{4} }*(-2sinxcosx)=- \frac{sin2x}{4 \sqrt[4]{(1+cos^2x)^3} }](https://tex.z-dn.net/?f=y%3D+%5Csqrt%5B4%5D%7B1%2Bcos%5E%7B2%7Dx%7D+%3D%281%2Bcos%5E%7B2%7Dx%29%5E%7B+%5Cfrac%7B1%7D%7B4%7D+%7D+%5C%5C+%0Ay%27%3D++%5Cfrac%7B1%7D%7B4%7D%281%2Bcos%5E2x%29%5E%7B+%5Cfrac%7B1%7D%7B4%7D-+%5Cfrac%7B4%7D%7B4%7D++%7D%2A%282cosx%2A%28-sinx%29%29%3D+%5C%5C+%3D+%5Cfrac%7B1%7D%7B4%7D%281%2Bcos%5E2x%29%5E%7B-+%5Cfrac%7B3%7D%7B4%7D+%7D%2A%28-2sinxcosx%29%3D-+%5Cfrac%7Bsin2x%7D%7B4+%5Csqrt%5B4%5D%7B%281%2Bcos%5E2x%29%5E3%7D+%7D++++)
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не понятно условие
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![y=(1+ \frac{1}{ \sqrt[3]{x} } )^3=(1+x^{- \frac{1}{3} })^3 \\ y'=3(1+ \frac{1}{ \sqrt[3]{x} } )^2*(- \frac{1}{3}x^{- \frac{4}{3} } )=- \frac{(1+ \frac{1}{ \sqrt[3]{x} })^2 }{ \sqrt[3]{x^4} } =- \frac{(1+ \frac{1}{ \sqrt[3]{x} } )^2}{x \sqrt[3]{x} }](https://tex.z-dn.net/?f=y%3D%281%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%5B3%5D%7Bx%7D+%7D+%29%5E3%3D%281%2Bx%5E%7B-+%5Cfrac%7B1%7D%7B3%7D+%7D%29%5E3+%5C%5C+%0Ay%27%3D3%281%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%5B3%5D%7Bx%7D+%7D+%29%5E2%2A%28-+%5Cfrac%7B1%7D%7B3%7Dx%5E%7B-+%5Cfrac%7B4%7D%7B3%7D+%7D+%29%3D-+%5Cfrac%7B%281%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%5B3%5D%7Bx%7D+%7D%29%5E2+%7D%7B+%5Csqrt%5B3%5D%7Bx%5E4%7D+%7D+%3D-+%5Cfrac%7B%281%2B+%5Cfrac%7B1%7D%7B+%5Csqrt%5B3%5D%7Bx%7D+%7D+%29%5E2%7D%7Bx+%5Csqrt%5B3%5D%7Bx%7D+%7D+)
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не понятно условие
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2.20