derivative of (3x^2/(5x+1))

Lösung

\frac{d}{d x} (\frac{3 x ^{2}}{5 x + 1})

\frac{3 ( 5 x ^{2} + 2 x )}{( 5 x + 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{3 x ^{2}}{5 x + 1})

Entferne die Konstante:

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

= 3 \frac{d}{d x} (\frac{x ^{2}}{5 x + 1})

Wende die Quotientenregel an:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 5 x + 1 ) - \frac{d}{d x} ( 5 x + 1 ) x ^{2}}{( 5 x + 1 ) ^{2}}

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

\frac{d}{d x} (5 x + 1) = 5

= 3 \cdot \frac{2 x ( 5 x + 1 ) - 5 x ^{2}}{( 5 x + 1 ) ^{2}}

Vereinfache

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

= \frac{3 ( 5 x ^{2} + 2 x )}{( 5 x + 1 ) ^{2}}

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