d/(dt)((x)(100(1-x^2)))

Lösung

\frac{d}{d t} ((t) (100 (1 - t^{2})))

100 (1 - 3 t^{2})

Schritte zur Lösung

\frac{d}{d t} ((t) (100 (1 - t^{2})))

Entferne die Konstante:

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

= 100 \frac{d}{d t} (t (1 - t^{2}))

Wende die Produktregel an:

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

f = t, g = 1 - t^{2}

= 100 (\frac{d t}{d t} (1 - t^{2}) + \frac{d}{d t} (1 - t^{2}) t)

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

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

= 100 (1 \cdot (1 - t^{2}) + (- 2 t) t)

Vereinfache

100 (1 \cdot (1 - t^{2}) + (- 2 t) t) : 100 (1 - 3 t^{2})

= 100 (1 - 3 t^{2})

e x p an d \frac{1}{1 + x}

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

e x p an d \frac{( 100 + x ) ( 56 + 3 x )}{35}

e x p an d \frac{[ 5 ( x - h ) ] - [ 5 x ^{2} ]}{h}

e x p an d (2^{6})^{x + 3}