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Beliebt Rechnen >

derivative f(x)=(2x^2-5x)/(3x+5)

Lösung

ableitung von

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

Lösung

\frac{6 x ^{2} + 20 x - 25}{( 3 x + 5 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (2 x^{2} - 5 x) = 4 x - 5

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

= \frac{( 4 x - 5 ) ( 3 x + 5 ) - 3 ( 2 x ^{2} - 5 x )}{( 3 x + 5 ) ^{2}}

Multipliziere aus

(4 x - 5) (3 x + 5) - 3 (2 x^{2} - 5 x) : 6 x^{2} + 20 x - 25

= \frac{6 x ^{2} + 20 x - 25}{( 3 x + 5 ) ^{2}}

Graph

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