9*cos(x^2-3x+2)...

July 2022 1 4 Report

Найти производную ф-ции y=((x-3)/(x+3))^1/9*cos(x^2-3x+2)

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$y=(\frac{x-3}{x+3})^{\frac{1}{9}}\cdot cos(x^2-3x+2)\\\\y'=\frac{1}{9}\cdot (\frac{x-3}{x+3})^{-\frac{8}{9}}\cdot \frac{x+3-(x-3)}{(x+3)^2}\cdot cos(x^2-3x+2)+\\\\+(\frac{x-3}{x+3})^{\frac{1}{9}}\cdot (-sin(x^2-3x+2))\cdot (2x-3)=\\\\=\frac{1}{9}\cdot (\frac{x+3}{x-3})^{\frac{8}{9}}\cdot \frac{6}{(x+3)^2}\cdot cos(x^2-3x+2)-(\frac{x-3}{x+3})^{\frac{1}{9}}\cdot (2x-3)\cdot sin(x^2-3x+2)$

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