d/(dt)((\sqrt[3]{t})/(t-6))

Lösung

\frac{d}{d t} (\frac{3 t}{t - 6})

\frac{t - 6 - 3 3 t t ^{\frac{2}{3}}}{3 t ^{\frac{2}{3}} ( t - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{3 t}{t - 6})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( 3 t ) ( t - 6 ) - \frac{d}{d t} ( t - 6 ) 3 t}{( t - 6 ) ^{2}}

\frac{d}{d t} (3 t) = \frac{1}{3 t ^{\frac{2}{3}}}

\frac{d}{d t} (t - 6) = 1

= \frac{\frac{1}{3 t ^{\frac{2}{3}}} ( t - 6 ) - 1 \cdot 3 t}{( t - 6 ) ^{2}}

Vereinfache

\frac{\frac{1}{3 t ^{\frac{2}{3}}} ( t - 6 ) - 1 \cdot 3 t}{( t - 6 ) ^{2}} : \frac{t - 6 - 3 3 t t ^{\frac{2}{3}}}{3 t ^{\frac{2}{3}} ( t - 6 ) ^{2}}

= \frac{t - 6 - 3 3 t t ^{\frac{2}{3}}}{3 t ^{\frac{2}{3}} ( t - 6 ) ^{2}}

x \to 0 lim (x^{4} ln (x))

s l o p e (- 2.4) (2.4)

\frac{\partial}{\partial x} (2^{x^{2}})

\frac{d}{d θ} (1 + cos (2 θ))

a re a x^{2}, 6 - x, [- 3, 2]