Предмет: Математика,
автор: semen0307
Вычислите производную функции
3 и 6
Приложения:

Ответы
Автор ответа:
0
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} } 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%2B%5Cfrac%7B5%7D%7Bx%5E4%7D%2B+%5Csqrt%5B3%5D%7Bx%5E2%7D+-+%5Cfrac%7B1%7D%7B+%5Csqrt%5B5%5D%7Bx%5E2%7D+%7D+%3D7-3x%5E%7B12%7D%2B5x%5E%7B-4%7D%2B+x%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D+-x%5E%7B-+%5Cfrac%7B2%7D%7B5%7D+%7D+%5C%5C%5C%5C+y%27%3D-36x%5E%7B11%7D-20x%5E%7B-5%7D%2B+%5Cfrac%7B2%7D%7B3%7D+x%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%2B%5Cfrac%7B2%7D%7B5%7Dx%5E%7B-%5Cfrac%7B7%7D%7B5%7D%7D%3D-36x%5E%7B11%7D-+%5Cfrac%7B20%7D%7Bx%5E5%7D+%2B%5Cfrac%7B2%7D%7B3+%5Csqrt%5B3%5D%7Bx%7D+%7D%2B%5Cfrac%7B2%7D%7B5+%5Csqrt%5B5%5D%7Bx%5E7%7D+%7D)
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} 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%3D%5Cfrac%7B5x%2A%5Csqrt%5B3%5D%7Bx%5E2%7D%7D%7B7%2A%5Csqrt%5B5%5D%7Bx%7D%7D%3D%5Cfrac%7B5x%2Ax%5E%7B+%5Cfrac%7B2%7D%7B3%7D+%7D%7D%7B7%2Ax%5E%7B+%5Cfrac%7B1%7D%7B5%7D+%7D%7D%3D%5Cfrac%7B5%7D%7B7%7Dx%5E%7B%5Cfrac%7B5%7D%7B3%7D-%5Cfrac%7B1%7D%7B5%7D%7D%3D%5Cfrac%7B5%7D%7B7%7Dx%5E%7B%5Cfrac%7B22%7D%7B15%7D%7D+%5C%5C%5C%5C+y%27%3D%5Cfrac%7B5%7D%7B7%7D%2A%5Cfrac%7B22%7D%7B15%7D%2Ax%5E%7B%5Cfrac%7B7%7D%7B15%7D%7D%3D%5Cfrac%7B22%7D%7B21%7D%5Csqrt%5B15%5D%7Bx%5E7%7D+)
6)
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