Question

Вычислите производную функции
3 и 6

Answer 1

3)
$y=7-3x^{12}+\frac{5}{x^4}+ \sqrt[3]{x^2} - \frac{1}{ \sqrt[5]{x^2} } =7-3x^{12}+5x^{-4}+ x^{ \frac{2}{3} } -x^{- \frac{2}{5} } \\\\ y'=-36x^{11}-20x^{-5}+ \frac{2}{3} x^{-\frac{1}{3}}+\frac{2}{5}x^{-\frac{7}{5}}=-36x^{11}- \frac{20}{x^5} +\frac{2}{3 \sqrt[3]{x} }+\frac{2}{5 \sqrt[5]{x^7} }$

6)
$y=\frac{5x*\sqrt[3]{x^2}}{7*\sqrt[5]{x}}=\frac{5x*x^{ \frac{2}{3} }}{7*x^{ \frac{1}{5} }}=\frac{5}{7}x^{\frac{5}{3}-\frac{1}{5}}=\frac{5}{7}x^{\frac{22}{15}} \\\\ y'=\frac{5}{7}*\frac{22}{15}*x^{\frac{7}{15}}=\frac{22}{21}\sqrt[15]{x^7}$