derivative y=x^2sqrt(8+x)

Lösung

ableitung von

y = x^{2} 8 + x

\frac{5 x ^{2} + 32 x}{2 8 + x}

Schritte zur Lösung

\frac{d}{d x} (x^{2} 8 + x)

Wende die Produktregel an:

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

f = x^{2}, g = 8 + x

= \frac{d}{d x} (x^{2}) 8 + x + \frac{d}{d x} (8 + x) x^{2}

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

\frac{d}{d x} (8 + x) = \frac{1}{2 8 + x}

= 2 x 8 + x + \frac{1}{2 8 + x} x^{2}

Vereinfache

2 x 8 + x + \frac{1}{2 8 + x} x^{2} : \frac{5 x ^{2} + 32 x}{2 8 + x}

= \frac{5 x ^{2} + 32 x}{2 8 + x}

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