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Beliebt Rechnen >

derivative f(x)=sqrt(x+2)*sqrt(x+2)

Lösung

ableitung von

f (x) = x + 2 \cdot x + 2

Lösung

1

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x + 2, g = x + 2

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

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

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

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

Vereinfache

\frac{1}{2 x + 2} x + 2 + \frac{1}{2 x + 2} x + 2 : 1

= 1

Graph

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