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Beliebt Rechnen >

derivative f(x)=sqrt(x)(3x-1)

Lösung

ableitung von

f (x) = x (3 x - 1)

Lösung

\frac{9 x - 1}{2 x}

Schritte zur Lösung

\frac{d}{d x} (x (3 x - 1))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 3 x - 1

= \frac{d}{d x} (x) (3 x - 1) + \frac{d}{d x} (3 x - 1) x

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

\frac{d}{d x} (3 x - 1) = 3

= \frac{1}{2 x} (3 x - 1) + 3 x

Vereinfache

\frac{1}{2 x} (3 x - 1) + 3 x : \frac{9 x - 1}{2 x}

= \frac{9 x - 1}{2 x}

Graph

Beliebte Beispiele

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\frac{d}{d x} ((3 x + 4)^{6})

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sum from n=1 to infinity of 1/(4+e^{-n)}

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