Question

Найти частные производные первого и второго порядка x^2y+cosx

Answer 1

$f(x,y) = x^2y + \cos x\\\\ \frac{\partial f}{\partial x} = 2xy - \sin x\\\\ \frac{\partial f}{\partial y} = x^2\\\\ \frac{\partial^2 f}{\partial y \partial x} = 2x\\\\ \frac{\partial^2 f}{\partial y^2} = 0\\\\ \frac{\partial^2 f}{\partial x^2} = 2y - \cos x$