derivative y=(8x^2+8x+4)/(sqrt(x))

Lösung

ableitung von

y = \frac{8 x ^{2} + 8 x + 4}{x}

\frac{12 x ^{2} + 4 x - 2}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 4}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} + 8 x + 4 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 8 x + 4) = 16 x + 8

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 8 ) x - \frac{1}{2 x} ( 8 x ^{2} + 8 x + 4 )}{( x ) ^{2}} : \frac{12 x ^{2} + 4 x - 2}{x x}

= \frac{12 x ^{2} + 4 x - 2}{x x}

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