d/(dt)((x)(1+4t-t^2))

Lösung

\frac{d}{d t} ((x) (1 + 4 t - t^{2}))

\frac{d x}{d t} (1 + 4 t - t^{2}) + (- 2 t + 4) x

Schritte zur Lösung

\frac{d}{d t} ((x) (1 + 4 t - t^{2}))

Wende die Produktregel an:

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

f = x, g = 1 + 4 t - t^{2}

= \frac{d x}{d t} (1 + 4 t - t^{2}) + \frac{d}{d t} (1 + 4 t - t^{2}) x

\frac{d}{d t} (1 + 4 t - t^{2}) = - 2 t + 4

= \frac{d x}{d t} (1 + 4 t - t^{2}) + (- 2 t + 4) x

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

e x p an d \frac{2 ^{2 x + 2}}{( 4 ^{x} + 1 ) ^{2}}

e x p an d (1 - 7) + (7 - 7)

e x p an d \frac{( s + 3 )}{( s + 2.5 ) ( s + 4 ) ^{2}}

e x p an d \frac{( s + 1 ) ( s - 2 )}{( s + 3 )}