(\partial)/(\partial y)(5x^2-3xy^2+xyz)

解

\frac{\partial}{\partial y} (5 x^{2} - 3 x y^{2} + x yz)

x z - 6 x y

解答ステップ

\frac{\partial}{\partial y} (5 x^{2} - 3 x y^{2} + x yz)

x, z

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial y} (5 x^{2}) - \frac{\partial}{\partial y} (3 x y^{2}) + \frac{\partial}{\partial y} (x yz)

\frac{\partial}{\partial y} (5 x^{2}) = 0

\frac{\partial}{\partial y} (3 x y^{2}) = 6 x y

\frac{\partial}{\partial y} (x yz) = x z

= 0 - 6 x y + x z

簡素化

= x z - 6 x y