Question

Найти полные дифференциалы указанных функций

Answer 1

$Z'x = y( {x}^{2} \sin(x) ) = y(2x \sin(x) + {x}^{2} \cos(x) )$

$Z'y = {x}^{2} \sin(x) - 3$

$Z''xx = y(2 \sin(x) + 2x \cos(x) + 2x \cos(x) - {x}^{2} \sin(x) ) = y(2 \sin(x) + 4x \cos(x) - {x}^{2} \sin(x) )$

$Z''yy = 0$

$Z''xy = Z''yx = ( {x}^{2} \sin(x) - 3)'x = 2x \sin(x) + {x}^{2} \cos(x)$

${d}^{2}z = y(2 \sin(x) + 4x \cos(x) - {x}^{2} \sin(x) )d {x}^{2} + (2x \sin(x) + {x}^{2} \cos(x) )dxdy + 0 \times d {y}^{2}$