Упр.186 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

1. $$y=-\frac{2}{x^4}=-2x^{-4}$$
   $$y’=-2\cdot(-4x^{-5})=\frac{8}{x^5}$$
2. $$y=4x^{-\frac{3}{2}}$$
   $$y’=4\cdot\left(-\frac{3}{2}x^{-\frac{5}{2}}\right)=-6x^{-\frac{5}{2}}=-\frac{6}{x^{5/2}}$$
3. $$y=x^{-\frac{3}{2}}+6x^{\frac{5}{6}}$$
   $$y’=-\frac{3}{2}x^{-\frac{5}{2}}+6\cdot\frac{5}{6}x^{-\frac{1}{6}}$$
   $$y’=-\frac{3}{2}x^{-\frac{5}{2}}+5x^{-\frac{1}{6}}$$
4. $$y=2\sqrt[7]{x^2}-3\sqrt[5]{x^{-2}}=2x^{\frac{2}{7}}-3x^{-\frac{2}{5}}$$
   $$y’=2\cdot\frac{2}{7}x^{-\frac{5}{7}}-3\cdot\left(-\frac{2}{5}x^{-\frac{7}{5}}\right)$$
   $$y’=\frac{4}{7}x^{-\frac{5}{7}}+\frac{6}{5}x^{-\frac{7}{5}}$$
5. $$y=6\sqrt[6]{x^5}-\frac{5}{\sqrt[5]{x^4}}=6x^{\frac{5}{6}}-5x^{-\frac{4}{5}}$$
   $$y’=6\cdot\frac{5}{6}x^{-\frac{1}{6}}-5\cdot\left(-\frac{4}{5}x^{-\frac{9}{5}}\right)$$
   $$y’=5x^{-\frac{1}{6}}+4x^{-\frac{9}{5}}$$
6. $$y=2x^3\sqrt[3]{x^2}+\frac{4}{x\sqrt[4]{x^3}}=2x^{\frac{11}{3}}+4x^{-\frac{7}{4}}$$
   $$y’=2\cdot\frac{11}{3}x^{\frac{8}{3}}+4\cdot\left(-\frac{7}{4}x^{-\frac{11}{4}}\right)$$
   $$y’=\frac{22}{3}x^{\frac{8}{3}}-7x^{-\frac{11}{4}}$$

Ответ

1. $$y’=\frac{8}{x^5}$$
2. $$y’=-\frac{6}{x^{5/2}}$$
3. $$y’=-\frac{3}{2}x^{-\frac{5}{2}}+5x^{-\frac{1}{6}}$$
4. $$y’=\frac{4}{7}x^{-\frac{5}{7}}+\frac{6}{5}x^{-\frac{7}{5}}$$
5. $$y’=5x^{-\frac{1}{6}}+4x^{-\frac{9}{5}}$$
6. $$y’=\frac{22}{3}x^{\frac{8}{3}}-7x^{-\frac{11}{4}}$$