derivative of (70x/((3x^2+8)^2))

Lösung

\frac{d}{d x} (\frac{70 x}{( 3 x ^{2} + 8 ) ^{2}})

\frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{70 x}{( 3 x ^{2} + 8 ) ^{2}})

Entferne die Konstante:

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

= 70 \frac{d}{d x} (\frac{x}{( 3 x ^{2} + 8 ) ^{2}})

Wende die Quotientenregel an:

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

= 70 \cdot \frac{\frac{d x}{d x} ( 3 x ^{2} + 8 ) ^{2} - \frac{d}{d x} ( ( 3 x ^{2} + 8 ) ^{2} ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((3 x^{2} + 8)^{2}) = 12 x (3 x^{2} + 8)

= 70 \cdot \frac{1 \cdot ( 3 x ^{2} + 8 ) ^{2} - 12 x ( 3 x ^{2} + 8 ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}}

Vereinfache

70 \cdot \frac{1 \cdot ( 3 x ^{2} + 8 ) ^{2} - 12 x ( 3 x ^{2} + 8 ) x}{( ( 3 x ^{2} + 8 ) ^{2} ) ^{2}} : \frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

= \frac{70 ( 8 - 9 x ^{2} )}{( 3 x ^{2} + 8 ) ^{3}}

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