(\partial)/(\partial x)(5(x-4)y^3)

解

\frac{\partial}{\partial x} (5 \cdot (x - 4) \cdot y^{3})

5 y^{3}

解答ステップ

\frac{\partial}{\partial x} (5 (x - 4) y^{3})

y

を定数として扱う

定数を除去:

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

= 5 y^{3} \frac{\partial}{\partial x} (x - 4)

和/差の法則を適用:

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

= 5 y^{3} (\frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (x) = 1

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

= 5 y^{3} (1 - 0)

簡素化

= 5 y^{3}