derivative y=(7x-24)/(x^2+2x)

Lösung

ableitung von

y = \frac{7 x - 24}{x ^{2} + 2 x}

\frac{- 7 x ^{2} + 48 x + 48}{( x ^{2} + 2 x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 x - 24}{x ^{2} + 2 x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 7 x - 24 ) ( x ^{2} + 2 x ) - \frac{d}{d x} ( x ^{2} + 2 x ) ( 7 x - 24 )}{( x ^{2} + 2 x ) ^{2}}

\frac{d}{d x} (7 x - 24) = 7

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

= \frac{7 ( x ^{2} + 2 x ) - ( 2 x + 2 ) ( 7 x - 24 )}{( x ^{2} + 2 x ) ^{2}}

Multipliziere aus

7 (x^{2} + 2 x) - (2 x + 2) (7 x - 24) : - 7 x^{2} + 48 x + 48

= \frac{- 7 x ^{2} + 48 x + 48}{( x ^{2} + 2 x ) ^{2}}

\int \frac{1}{3 x ^{6}} d x

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