d/(dt)((x)(1-sqrt(t)))

Lösung

\frac{d}{d t} ((x) (1 - t))

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

Schritte zur Lösung

\frac{d}{d t} ((x) (1 - t))

Wende die Produktregel an:

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

f = x, g = 1 - t

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

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

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

Vereinfache

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

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

e x p an d \frac{2 ( 3 π - 4 ) a ^{3}}{9}

e x p an d π (6 - \frac{ln ( 2 )}{16})

e x p an d \frac{5 z ^{2} + 2 z + 3}{( z + 2 ) ( z - 1 )}

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

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