d/(ds)((k)(s^2+2s+4+s^2k+5sk-9k))

解

\frac{d}{d s} ((k) (s^{2} + 2 s + 4 + s^{2} k + 5 s k - 9 k))

k (2 s + 2 s k + 5 k + 2)

解答ステップ

\frac{d}{d s} ((k) (s^{2} + 2 s + 4 + s^{2} k + 5 s k - 9 k))

定数を除去:

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

= k \frac{d}{d s} (s^{2} + 2 s + 4 + s^{2} k + 5 s k - 9 k)

和/差の法則を適用:

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

= k (\frac{d}{d s} (s^{2}) + \frac{d}{d s} (2 s) + \frac{d}{d s} (4) + \frac{d}{d s} (s^{2} k) + \frac{d}{d s} (5 s k) - \frac{d}{d s} (9 k))

\frac{d}{d s} (s^{2}) = 2 s

\frac{d}{d s} (2 s) = 2

\frac{d}{d s} (4) = 0

\frac{d}{d s} (s^{2} k) = 2 k s

\frac{d}{d s} (5 s k) = 5 k

\frac{d}{d s} (9 k) = 0

= k (2 s + 2 + 0 + 2 k s + 5 k - 0)

簡素化

= k (2 s + 2 s k + 5 k + 2)