d/(dt)((x)(4t-x))

Lösung

\frac{d}{d t} ((x) (4 t - x))

4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

Schritte zur Lösung

\frac{d}{d t} ((x) (4 t - x))

Wende die Produktregel an:

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

f = x, g = 4 t - x

= \frac{d x}{d t} (4 t - x) + \frac{d}{d t} (4 t - x) x

\frac{d}{d t} (4 t - x) = 4 - \frac{d x}{d t}

= \frac{d x}{d t} (4 t - x) + (4 - \frac{d x}{d t}) x

Vereinfache

\frac{d x}{d t} (4 t - x) + (4 - \frac{d x}{d t}) x : 4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

= 4 t \frac{d x}{d t} - 2 x \frac{d x}{d t} + 4 x

e x p an d (x + Δ x)^{2} - 2 (x + Δ x) + 3

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

e x p an d \frac{8}{8 - 7}

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

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