Question

Найти частные производные функции:

Answer 1

$z=ln\, tg^3(\frac{x^2}{3}-\frac{y}{6})\\\\z'_{x}=\frac{1}{tg^3(\frac{x^2}{3}-\frac{y}{6})}\cdot 3tg^2( \frac{x^2}{3}-\frac{y}{6})\cdot \frac{1}{cos^2(\frac{x^2}{3}-\frac{y}{6})}\cdot \frac{2}{3}x$

$z'_{y}=\frac{1}{tg^3(\frac{x^2}{3}-\frac{y}{6})}\cdot 3tg^2(\frac{x^2}{3}-\frac{y}{6})\cdot \frac{1}{cos^2(\frac{x^2}{3}-\frac{y}{6})}\cdot \frac{-1}{6}$