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Beliebt Rechnen >

derivative f(x)=sqrt(x)(x-10)

Lösung

ableitung von

f (x) = x (x - 10)

Lösung

\frac{3 x - 10}{2 x}

Schritte zur Lösung

\frac{d}{d x} (x (x - 10))

Wende die Produktregel an:

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

f = x, g = x - 10

= \frac{d}{d x} (x) (x - 10) + \frac{d}{d x} (x - 10) x

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

\frac{d}{d x} (x - 10) = 1

= \frac{1}{2 x} (x - 10) + 1 \cdot x

Vereinfache

\frac{1}{2 x} (x - 10) + 1 \cdot x : \frac{3 x - 10}{2 x}

= \frac{3 x - 10}{2 x}

Graph

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