(\partial)/(\partial x)(x^2y+2xz+2y^2+6z+9)

解

\frac{\partial}{\partial x} (x^{2} y + 2 x z + 2 y^{2} + 6 z + 9)

2 x y + 2 z

解答ステップ

\frac{\partial}{\partial x} (x^{2} y + 2 x z + 2 y^{2} + 6 z + 9)

y, 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 x} (x^{2} y) + \frac{\partial}{\partial x} (2 x z) + \frac{\partial}{\partial x} (2 y^{2}) + \frac{\partial}{\partial x} (6 z) + \frac{\partial}{\partial x} (9)

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

\frac{\partial}{\partial x} (2 x z) = 2 z

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

\frac{\partial}{\partial x} (6 z) = 0

\frac{\partial}{\partial x} (9) = 0

= 2 y x + 2 z + 0 + 0 + 0

簡素化

= 2 x y + 2 z