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

解

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

2 x

解答ステップ

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

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

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

= 2 x + 0 + 0

簡素化

= 2 x