Вычислите производную функции
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Ответил SRT1905
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3)
![y=7-3x^{12}+frac{5}{x^4}+ sqrt[3]{x^2} - frac{1}{ sqrt[5]{x^2} } =7-3x^{12}+5x^{-4}+ x^{ frac{2}{3} } -x^{- frac{2}{5} } \\ y'=-36x^{11}-20x^{-5}+ frac{2}{3} x^{-frac{1}{3}}+frac{2}{5}x^{-frac{7}{5}}=-36x^{11}- frac{20}{x^5} +frac{2}{3 sqrt[3]{x} }+frac{2}{5 sqrt[5]{x^7} }](https://tex.z-dn.net/?f=y%3D7-3x%5E%7B12%7D%2Bfrac%7B5%7D%7Bx%5E4%7D%2B+sqrt%5B3%5D%7Bx%5E2%7D+-+frac%7B1%7D%7B+sqrt%5B5%5D%7Bx%5E2%7D+%7D+%3D7-3x%5E%7B12%7D%2B5x%5E%7B-4%7D%2B+x%5E%7B+frac%7B2%7D%7B3%7D+%7D+-x%5E%7B-+frac%7B2%7D%7B5%7D+%7D+%5C%5C+y%27%3D-36x%5E%7B11%7D-20x%5E%7B-5%7D%2B+frac%7B2%7D%7B3%7D+x%5E%7B-frac%7B1%7D%7B3%7D%7D%2Bfrac%7B2%7D%7B5%7Dx%5E%7B-frac%7B7%7D%7B5%7D%7D%3D-36x%5E%7B11%7D-+frac%7B20%7D%7Bx%5E5%7D+%2Bfrac%7B2%7D%7B3+sqrt%5B3%5D%7Bx%7D+%7D%2Bfrac%7B2%7D%7B5+sqrt%5B5%5D%7Bx%5E7%7D+%7D "y=7-3x^{12}+frac{5}{x^4}+ sqrt[3]{x^2} - frac{1}{ sqrt[5]{x^2} } =7-3x^{12}+5x^{-4}+ x^{ frac{2}{3} } -x^{- frac{2}{5} } \\ y'=-36x^{11}-20x^{-5}+ frac{2}{3} x^{-frac{1}{3}}+frac{2}{5}x^{-frac{7}{5}}=-36x^{11}- frac{20}{x^5} +frac{2}{3 sqrt[3]{x} }+frac{2}{5 sqrt[5]{x^7} }")
6)
![y=frac{5x*sqrt[3]{x^2}}{7*sqrt[5]{x}}=frac{5x*x^{ frac{2}{3} }}{7*x^{ frac{1}{5} }}=frac{5}{7}x^{frac{5}{3}-frac{1}{5}}=frac{5}{7}x^{frac{22}{15}} \\ y'=frac{5}{7}*frac{22}{15}*x^{frac{7}{15}}=frac{22}{21}sqrt[15]{x^7}](https://tex.z-dn.net/?f=y%3Dfrac%7B5x%2Asqrt%5B3%5D%7Bx%5E2%7D%7D%7B7%2Asqrt%5B5%5D%7Bx%7D%7D%3Dfrac%7B5x%2Ax%5E%7B+frac%7B2%7D%7B3%7D+%7D%7D%7B7%2Ax%5E%7B+frac%7B1%7D%7B5%7D+%7D%7D%3Dfrac%7B5%7D%7B7%7Dx%5E%7Bfrac%7B5%7D%7B3%7D-frac%7B1%7D%7B5%7D%7D%3Dfrac%7B5%7D%7B7%7Dx%5E%7Bfrac%7B22%7D%7B15%7D%7D+%5C%5C+y%27%3Dfrac%7B5%7D%7B7%7D%2Afrac%7B22%7D%7B15%7D%2Ax%5E%7Bfrac%7B7%7D%7B15%7D%7D%3Dfrac%7B22%7D%7B21%7Dsqrt%5B15%5D%7Bx%5E7%7D+ "y=frac{5x*sqrt[3]{x^2}}{7*sqrt[5]{x}}=frac{5x*x^{ frac{2}{3} }}{7*x^{ frac{1}{5} }}=frac{5}{7}x^{frac{5}{3}-frac{1}{5}}=frac{5}{7}x^{frac{22}{15}} \\ y'=frac{5}{7}*frac{22}{15}*x^{frac{7}{15}}=frac{22}{21}sqrt[15]{x^7}")
6)
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