Question

Найти дифференциал функции.

Answer 1

Ответ:

$z = \sin( {x}^{2} + {y}^{2} )$

$\frac{dz}{dx} = \cos( {x}^{2} + {y}^{2} ) \times 2x$

$\frac{dz}{dy} = \cos( {x}^{2} + {y}^{2} ) \times 2y$

$dz = \cos( {x}^{2} + {y}^{2} ) \times 2xdx + \cos( {x}^{2} + {y}^{2} ) \times 2ydy = \cos( {x}^{2} + {y}^{2} ) (2xdx + 2ydy) = 2 \cos( {x}^{2} + {y}^{2} ) (xdx + ydy)$