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Beliebt Rechnen >

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

Lösung

ableitung von

f (x) = x (x^{3} - x)

Lösung

\frac{7 x ^{2} x - 3 x}{2}

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = x^{3} - x

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

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

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

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

Vereinfache

\frac{1}{2 x} (x^{3} - x) + (3 x^{2} - 1) x : \frac{7 x ^{2} x - 3 x}{2}

= \frac{7 x ^{2} x - 3 x}{2}

Graph

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