(\partial)/(\partial x)((z)(2x^4+y^4+z^3))

解

\frac{\partial}{\partial x} ((z) (2 x^{4} + y^{4} + z^{3}))

8 z x^{3}

解答ステップ

\frac{\partial}{\partial x} ((z) (2 x^{4} + y^{4} + z^{3}))

z, y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{\partial}{\partial x} (2 x^{4} + y^{4} + z^{3})

和/差の法則を適用:

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

= z (\frac{\partial}{\partial x} (2 x^{4}) + \frac{\partial}{\partial x} (y^{4}) + \frac{\partial}{\partial x} (z^{3}))

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

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

\frac{\partial}{\partial x} (z^{3}) = 0

= z (8 x^{3} + 0 + 0)

簡素化

= 8 z x^{3}