Y=- найти производную

Question 1

Question 2

Решение:

$\displaystyle \Big (y \Big )' = \Big (5 \sqrt[4]{x} - 7 \sqrt[6]{x} \Big )' = \Big (5 x^{\frac {1}{4}} - 7 x^{\frac{1}{6}} \Big )' = 5 \cdot \Big (x^{\frac{1}{4}} \Big )' - 7 \cdot \Big (x^{\frac{1}{6}} \Big )' =\\\\= 5 \cdot \frac{1}{4} \cdot \Big (x^{-\frac{3}{4}} \Big ) - 7 \cdot \frac{1}{6} \cdot \Big (x^{-\frac{5}{6} } \Big ) = \frac{5}{4} \cdot \bigg ( \frac{1}{x^{\frac{3}{4}} } \bigg ) - \frac{7}{6} \cdot \bigg ( \frac{1}{x^{\frac{5}{6}}} \bigg ) = \\\\$

$\displaystyle \large {\boxed{ = \;\; \frac{5}{4x^{\frac{3}{4}} } - \frac{7}{6x^{\frac{5}{6}}} \;\; = \;\; \frac{5}{4 \sqrt[4]{x^3} } - \frac{7}{6 \sqrt[6]{x^5} } }}$