d/(dt)((ln(2t-1))/(t^2-1))

Lösung

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

\frac{2 ( t ^{2} - 1 ) - 2 t ln ( 2 t - 1 ) ( 2 t - 1 )}{( 2 t - 1 ) ( t ^{2} - 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{2}{2 t - 1} ( t ^{2} - 1 ) - 2 t ln ( 2 t - 1 )}{( t ^{2} - 1 ) ^{2}} : \frac{2 ( t ^{2} - 1 ) - 2 t ln ( 2 t - 1 ) ( 2 t - 1 )}{( 2 t - 1 ) ( t ^{2} - 1 ) ^{2}}

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

\frac{\partial}{\partial x} (2 x^{2} - 3 x y + z - 4)

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\frac{d}{d x} (x^{7} + 7 x^{2})