(\partial)/(\partial x)(4xy-10x^2y^2z+5z^2)

解

\frac{\partial}{\partial x} (4 x y - 10 x^{2} y^{2} z + 5 z^{2})

- 20 x y^{2} z + 4 y

解答ステップ

\frac{\partial}{\partial x} (4 x y - 10 x^{2} y^{2} z + 5 z^{2})

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} (4 x y) - \frac{\partial}{\partial x} (10 x^{2} y^{2} z) + \frac{\partial}{\partial x} (5 z^{2})

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (10 x^{2} y^{2} z) = 20 y^{2} z x

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

= 4 y - 20 y^{2} z x + 0

簡素化

= - 20 x y^{2} z + 4 y