d/(dt)((a(t))(a(t)^4+t^4-6a(t)^2t))

Lösung

\frac{d}{d t} ((a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t))

a (5 a t^{4} + 5 t^{4} - 24 a t^{3})

Schritte zur Lösung

\frac{d}{d t} ((a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t))

Vereinfache

(a (t)) (a (t)^{4} + t^{4} - 6 a (t)^{2} t) : a t (a t^{4} + t^{4} - 6 a t^{3})

= \frac{d}{d t} (a t (a t^{4} + t^{4} - 6 a t^{3}))

Entferne die Konstante:

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

= a \frac{d}{d t} (t (a t^{4} + t^{4} - 6 a t^{3}))

Wende die Produktregel an:

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

f = t, g = a t^{4} + t^{4} - 6 a t^{3}

= a (\frac{d t}{d t} (a t^{4} + t^{4} - 6 a t^{3}) + \frac{d}{d t} (a t^{4} + t^{4} - 6 a t^{3}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (a t^{4} + t^{4} - 6 a t^{3}) = 4 a t^{3} + 4 t^{3} - 18 a t^{2}

= a (1 \cdot (a t^{4} + t^{4} - 6 a t^{3}) + (4 a t^{3} + 4 t^{3} - 18 a t^{2}) t)

Vereinfache

a (1 \cdot (a t^{4} + t^{4} - 6 a t^{3}) + (4 a t^{3} + 4 t^{3} - 18 a t^{2}) t) : a (5 a t^{4} + 5 t^{4} - 24 a t^{3})

= a (5 a t^{4} + 5 t^{4} - 24 a t^{3})

e x p an d \frac{j + 2}{( - 2 + j ) ( j - 1 ) ( j ^{2} + 2 j + 5 )}

e x p an d (3^{^{'}} x^{2^{^{'}}} - 6 x + 4) (- 2 x^{2} + 7 x + 5)^{^{'}}

e x p an d \frac{( 3 + 9 x )}{( 1 + x ) ( 3 + 5 x )}

s im pl i f y 3 2 e^{(a + b) i} - 5 i

s im pl i f y 2 (- 2 + 6)