d/(dt)(({p}(t,m))(k{p}(t,m)(1-m-({p}(t,m))/A)))

解

\frac{d}{d t} ((p (t, m)) (k p (t, m) (1 - m - \frac{p ( t , m )}{A})))

k (\frac{d}{d t} (p (t, m)) p (t, m) (1 - m - \frac{p ( t , m )}{A}) + (\frac{d}{d t} (p (t, m)) (1 - m - \frac{p ( t , m )}{A}) + (0 - 0 - \frac{1}{A} \frac{d}{d t} (p (t, m))) p (t, m)) p (t, m))

解答ステップ

\frac{d}{d t} ((p (t, m)) (k p (t, m) (1 - m - \frac{p ( t , m )}{A})))

定数を除去:

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

= k \frac{d}{d t} (p (t, m) p (t, m) (1 - m - \frac{p ( t , m )}{A}))

積の法則を適用:

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

f = p (t, m), g = p (t, m) (1 - m - \frac{p ( t , m )}{A})

= k (\frac{d}{d t} (p (t, m)) p (t, m) (1 - m - \frac{p ( t , m )}{A}) + \frac{d}{d t} (p (t, m) (1 - m - \frac{p ( t , m )}{A})) p (t, m))

\frac{d}{d t} (p (t, m) (1 - m - \frac{p ( t , m )}{A})) = \frac{d}{d t} (p (t, m)) (1 - m - \frac{p ( t , m )}{A}) + (0 - 0 - \frac{1}{A} \frac{d}{d t} (p (t, m))) p (t, m)

= k (\frac{d}{d t} (p (t, m)) p (t, m) (1 - m - \frac{p ( t , m )}{A}) + (\frac{d}{d t} (p (t, m)) (1 - m - \frac{p ( t , m )}{A}) + (0 - 0 - \frac{1}{A} \frac{d}{d t} (p (t, m))) p (t, m)) p (t, m))