derivative of (2x^2/(x-2))

Lösung

\frac{d}{d x} (\frac{2 x ^{2}}{x - 2})

\frac{2 ( x ^{2} - 4 x )}{( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{2 x ^{2}}{x - 2})

Entferne die Konstante:

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

= 2 \frac{d}{d x} (\frac{x ^{2}}{x - 2})

Wende die Quotientenregel an:

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

= 2 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) x ^{2}}{( x - 2 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 \cdot \frac{2 x ( x - 2 ) - 1 \cdot x ^{2}}{( x - 2 ) ^{2}}

Vereinfache

2 \cdot \frac{2 x ( x - 2 ) - 1 \cdot x ^{2}}{( x - 2 ) ^{2}} : \frac{2 ( x ^{2} - 4 x )}{( x - 2 ) ^{2}}

= \frac{2 ( x ^{2} - 4 x )}{( x - 2 ) ^{2}}

\frac{\partial}{\partial x} (ln (\frac{y ^{6}}{x ^{10}}))

\int 4 x^{2} e^{2 x} d x

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