d/(dt)(({P}(t,a,b))(a{P}(t,a,b)(b-{P}(t,a,b))))

解

\frac{d}{d t} ((P (t, a, b)) (a P (t, a, b) (b - P (t, a, b))))

a (\frac{d}{d t} (P (t, a, b)) P (t, a, b) (b - P (t, a, b)) + (\frac{d}{d t} (P (t, a, b)) (b - P (t, a, b)) + (0 - \frac{d}{d t} (P (t, a, b))) P (t, a, b)) P (t, a, b))

解答ステップ

\frac{d}{d t} ((P (t, a, b)) (a P (t, a, b) (b - P (t, a, b))))

定数を除去:

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

= a \frac{d}{d t} (P (t, a, b) P (t, a, b) (b - P (t, a, b)))

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = P (t, a, b), g = P (t, a, b) (b - P (t, a, b))

= a (\frac{d}{d t} (P (t, a, b)) P (t, a, b) (b - P (t, a, b)) + \frac{d}{d t} (P (t, a, b) (b - P (t, a, b))) P (t, a, b))

\frac{d}{d t} (P (t, a, b) (b - P (t, a, b))) = \frac{d}{d t} (P (t, a, b)) (b - P (t, a, b)) + (0 - \frac{d}{d t} (P (t, a, b))) P (t, a, b)

= a (\frac{d}{d t} (P (t, a, b)) P (t, a, b) (b - P (t, a, b)) + (\frac{d}{d t} (P (t, a, b)) (b - P (t, a, b)) + (0 - \frac{d}{d t} (P (t, a, b))) P (t, a, b)) P (t, a, b))