Z= ln(3x+y) найти производные первого и второго порядка.

Первого порядка [latex]\frac{\partial z}{\partial x}= \frac{1}{3x+y} *3=\frac{3}{3x+y} ;\\ \frac{\partial z}{\partial y}= \frac{1}{3x+y} *1=\frac{1}{3x+y} .[/latex] Второго порядка [latex] \frac{\partial^2 z}{\partial x^2}= -\frac{3}{(3x+y)^2} *3=-\frac{9}{(3x+y)^2}; \\ \frac{\partial^2 z}{\partial y^2}= -\frac{1}{(3x+y)^2} *1=-\frac{1}{(3x+y)^2}; \\ \frac{\partial^2 z}{\partial x \partial y}= -\frac{3}{(3x+y)^2} *1=-\frac{3}{(3x+y)^2}; \\ \frac{\partial^2 z}{\partial y \partial x}= -\frac{1}{(3x+y)^2} *3=-\frac{3}{(3x+y)^2}[/latex]