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Beliebt Rechnen >

derivative f(x)=(6x^2-1)/(2sqrt(x))

Lösung

ableitung von

f (x) = \frac{6 x ^{2} - 1}{2 x}

Lösung

\frac{18 x ^{2} + 1}{4 x x}

Schritte zur Lösung

\frac{d}{d x} (\frac{6 x ^{2} - 1}{2 x})

Entferne die Konstante:

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

= \frac{1}{2} \frac{d}{d x} (\frac{6 x ^{2} - 1}{x})

Wende die Quotientenregel an:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 6 x ^{2} - 1 ) x - \frac{d}{d x} ( x ) ( 6 x ^{2} - 1 )}{( x ) ^{2}}

\frac{d}{d x} (6 x^{2} - 1) = 12 x

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

= \frac{1}{2} \cdot \frac{12 x x - \frac{1}{2 x} ( 6 x ^{2} - 1 )}{( x ) ^{2}}

Vereinfache

\frac{1}{2} \cdot \frac{12 x x - \frac{1}{2 x} ( 6 x ^{2} - 1 )}{( x ) ^{2}} : \frac{18 x ^{2} + 1}{4 x x}

= \frac{18 x ^{2} + 1}{4 x x}

Graph

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