(\partial)/(\partial x)(r+2r^4x+4x)

解

\frac{\partial}{\partial x} (r + 2 r^{4} x + 4 x)

2 r^{4} + 4

解答ステップ

\frac{\partial}{\partial x} (r + 2 r^{4} x + 4 x)

r

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} (r) + \frac{\partial}{\partial x} (2 r^{4} x) + \frac{\partial}{\partial x} (4 x)

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

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

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

= 0 + 2 r^{4} + 4

簡素化

= 2 r^{4} + 4