d/(dt)((x)(2{r}(t)-5x))

Lösung

\frac{d}{d t} ((x) (2 r (t) - 5 x))

- 10 x \frac{d x}{d t} + 2 r (t) \frac{d x}{d t} + 2 x \frac{d}{d t} (r (t))

Schritte zur Lösung

\frac{d}{d t} ((x) (2 r (t) - 5 x))

Wende die Produktregel an:

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

f = x, g = 2 r (t) - 5 x

= \frac{d x}{d t} (2 r (t) - 5 x) + \frac{d}{d t} (2 r (t) - 5 x) x

\frac{d}{d t} (2 r (t) - 5 x) = 2 \frac{d}{d t} (r (t)) - 5 \frac{d x}{d t}

= \frac{d x}{d t} (2 r (t) - 5 x) + (2 \frac{d}{d t} (r (t)) - 5 \frac{d x}{d t}) x

Vereinfache

\frac{d x}{d t} (2 r (t) - 5 x) + (2 \frac{d}{d t} (r (t)) - 5 \frac{d x}{d t}) x : - 10 x \frac{d x}{d t} + 2 r (t) \frac{d x}{d t} + 2 x \frac{d}{d t} (r (t))

= - 10 x \frac{d x}{d t} + 2 r (t) \frac{d x}{d t} + 2 x \frac{d}{d t} (r (t))

e x p an d 2 (3 x + 2 = 6 x + 4)

e x p an d \frac{f ( x + 2 h ) - 2 x + 5}{4 h}

e x p an d \frac{( 2 - x ) ^{5}}{( x - 9 )}

e x p an d \frac{( 3 y - 8 ) ^{2}}{25}

e x p an d (x^{3} - 27) \circ (x - 1)