Question

Найдите производные от функции

Answer 1

$y=ctg^3\left (lg \frac{1+\sqrt{x}}{x^2+e^{-x}} \right )\\\\y'=3ctg^2\left (lg \frac{1+\sqrt{x}}{x^2+e^{-x}} \right )\cdot \frac{-1}{sin^2\left (lg \frac{1+\sqrt{x}}{x^2+e^{-x}} \right )} \cdot \frac{x^2+e^{-x}}{\left (1+\sqrt{x}\right )ln10} \cdot \\\\\cdot \frac{\frac{1}{2\sqrt{x}}(x^2+e^{-x})-(1+\sqrt{x})(2x-e^{-x})}{(x^2+e^{-x})^2}$