derivative of (0.2x/(x^2+9))

Lösung

\frac{d}{d x} (\frac{0.2 x}{x ^{2} + 9})

\frac{0.2 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{0.2 x}{x ^{2} + 9})

Entferne die Konstante:

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

= 0.2 \frac{d}{d x} (\frac{x}{x ^{2} + 9})

Wende die Quotientenregel an:

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

= 0.2 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 9 ) - \frac{d}{d x} ( x ^{2} + 9 ) x}{( x ^{2} + 9 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 9) = 2 x

= 0.2 \cdot \frac{1 \cdot ( x ^{2} + 9 ) - 2 xx}{( x ^{2} + 9 ) ^{2}}

Vereinfache

0.2 \cdot \frac{1 \cdot ( x ^{2} + 9 ) - 2 xx}{( x ^{2} + 9 ) ^{2}} : \frac{0.2 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

= \frac{0.2 ( - x ^{2} + 9 )}{( x ^{2} + 9 ) ^{2}}

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