derivative (x^3)/(10(x-2))

Lösung

ableitung von

\frac{x ^{3}}{10 ( x - 2 )}

\frac{x ^{2} ( x - 3 )}{5 ( x - 2 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{3}}{10 ( x - 2 )})

Entferne die Konstante:

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

= \frac{1}{10} \frac{d}{d x} (\frac{x ^{3}}{x - 2})

Wende die Quotientenregel an:

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

= \frac{1}{10} \cdot \frac{\frac{d}{d x} ( x ^{3} ) ( x - 2 ) - \frac{d}{d x} ( x - 2 ) x ^{3}}{( x - 2 ) ^{2}}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= \frac{1}{10} \cdot \frac{3 x ^{2} ( x - 2 ) - 1 \cdot x ^{3}}{( x - 2 ) ^{2}}

Vereinfache

\frac{1}{10} \cdot \frac{3 x ^{2} ( x - 2 ) - 1 \cdot x ^{3}}{( x - 2 ) ^{2}} : \frac{x ^{2} ( x - 3 )}{5 ( x - 2 ) ^{2}}

= \frac{x ^{2} ( x - 3 )}{5 ( x - 2 ) ^{2}}

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