derivative (x^2-7)sqrt(x)

Lösung

ableitung von

(x^{2} - 7) x

\frac{5 x ^{2} - 7}{2 x}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 7) x)

Wende die Produktregel an:

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

f = x^{2} - 7, g = x

= \frac{d}{d x} (x^{2} - 7) x + \frac{d}{d x} (x) (x^{2} - 7)

\frac{d}{d x} (x^{2} - 7) = 2 x

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

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

Vereinfache

2 x x + \frac{1}{2 x} (x^{2} - 7) : \frac{5 x ^{2} - 7}{2 x}

= \frac{5 x ^{2} - 7}{2 x}

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