derivative of (8x^2+6x+8/(sqrt(x)))

Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 8}{x})

\frac{12 x ^{2} + 3 x - 4}{x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{8 x ^{2} + 6 x + 8}{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} + 6 x + 8 ) x - \frac{d}{d x} ( x ) ( 8 x ^{2} + 6 x + 8 )}{( x ) ^{2}}

\frac{d}{d x} (8 x^{2} + 6 x + 8) = 16 x + 6

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

= \frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 8 )}{( x ) ^{2}}

Vereinfache

\frac{( 16 x + 6 ) x - \frac{1}{2 x} ( 8 x ^{2} + 6 x + 8 )}{( x ) ^{2}} : \frac{12 x ^{2} + 3 x - 4}{x x}

= \frac{12 x ^{2} + 3 x - 4}{x x}

\int_{\frac{2}{4}}^{\frac{1}{2}} \frac{1}{x ^{5} 16 x ^{2} - 1} d x

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