d/(dc)((t)(ce^{r(t,c)t}))

Lösung

\frac{d}{d c} ((t) (c e^{r (t, c) t}))

t (1 \cdot e^{r (t, c) t} + e^{r (t, c) t} t \frac{d}{d c} (r (t, c)) c)

Schritte zur Lösung

\frac{d}{d c} ((t) (c e^{r (t, c) t}))

Behandle

t

als Konstante

Entferne die Konstante:

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

= t \frac{d}{d c} (c e^{r (t, c) t})

Wende die Produktregel an:

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

f = c, g = e^{r (t, c) t}

= t (\frac{d c}{d c} e^{r (t, c) t} + \frac{d}{d c} (e^{r (t, c) t}) c)

\frac{d c}{d c} = 1

\frac{d}{d c} (e^{r (t, c) t}) = e^{r (t, c) t} t \frac{d}{d c} (r (t, c))

= t (1 \cdot e^{r (t, c) t} + e^{r (t, c) t} t \frac{d}{d c} (r (t, c)) c)

f a c t or d t (- t)

f a c t or 4 (a^{2} \cdot p q^{3})

f a c t or (8 m^{3} - 1) + (4 m^{2} + 5 m)

s im pl i f y C (90.17)

f a c t or 1 + x + 1