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

Lösung

\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))

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(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))

e x p an d sin (2) (x + 30 \circ) + cos (2) (x + 30 \circ)

e x p an d \frac{2}{( x - 1 ) ( x + 1 )}

s im pl i f y 4 lo g_{3} (x + 2) - 6 lo g_{3} (12) (x - 1)

s im pl i f y (x - 1 + 5) (x - 1 - 5)

s im pl i f y (cos (θ) + i sin (θ))^{7}