Question

Хотя б одно, прошу. Даю много баллов

Answer 1

Решение во вложении:

Answer 2

$1)\; \; y=x^6-5x^{3/5}-2x+3\; \; ,\; \; \; \boxed{x^{n}=n\cdot x^{n-1}}\\\\y'=6x^5-5\cdot \frac{3}{5}\cdot x^{-\frac{2}{5}}-2=6x^5-3x^{-\frac{2}{5}}-2\\\\2)\; \; y=\frac{5x^{2/3}}{6\sqrt{x}}=\frac{5}{6}\cdot x^{\frac{2}{3}-\frac{1}{2}}=\frac{5}{6}\cdot x^{\frac{1}{6}}\\\\y'=\frac{5}{6}\cdot \frac{1}{6}\cdot x^{-\frac{5}{6}}=\frac{5}{36}\cdot x^{-\frac{5}{6}}\\\\3)\; \; y=\frac{8x^3-x}{3x^2+4}\\\\y'=\frac{(24x^2-1)(3x^2+4)-(8x^3-x)\cdot 6x}{(3x^2+4)^2}=\frac{24x^4+99x^2-4}{(3x^2+4)^2}$

$y'(-5)=\frac{24\cdot 625+99\cdot 25-4}{(3\cdot 25+4)^2}=\frac{17471}{6241}$