derivative-(12x)/((6x^2+5)^2)

Lösung

ableitung von

- \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}}

- \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{12 x}{( 6 x ^{2} + 5 ) ^{2}})

Entferne die Konstante:

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

= - 12 \frac{d}{d x} (\frac{x}{( 6 x ^{2} + 5 ) ^{2}})

Wende die Quotientenregel an:

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

= - 12 \cdot \frac{\frac{d x}{d x} ( 6 x ^{2} + 5 ) ^{2} - \frac{d}{d x} ( ( 6 x ^{2} + 5 ) ^{2} ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((6 x^{2} + 5)^{2}) = 24 x (6 x^{2} + 5)

= - 12 \cdot \frac{1 \cdot ( 6 x ^{2} + 5 ) ^{2} - 24 x ( 6 x ^{2} + 5 ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}}

Vereinfache

- 12 \cdot \frac{1 \cdot ( 6 x ^{2} + 5 ) ^{2} - 24 x ( 6 x ^{2} + 5 ) x}{( ( 6 x ^{2} + 5 ) ^{2} ) ^{2}} : - \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

= - \frac{12 ( 5 - 18 x ^{2} )}{( 6 x ^{2} + 5 ) ^{3}}

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