(\partial)/(\partial r)((x)(r+3s-t))

解

\frac{\partial}{\partial r} ((x) (r + 3 s - t))

x

解答ステップ

\frac{\partial}{\partial r} ((x) (r + 3 s - t))

x, s, t

を定数として扱う

定数を除去:

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

= x \frac{\partial}{\partial r} (r + 3 s - t)

和/差の法則を適用:

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

= x (\frac{\partial}{\partial r} (r) + \frac{\partial}{\partial r} (3 s) - \frac{\partial}{\partial r} (t))

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

\frac{\partial}{\partial r} (3 s) = 0

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

= x (1 + 0 - 0)

簡素化

= x