derivative (x+1)(7sqrt(x)+2)

Lösung

ableitung von

(x + 1) (7 x + 2)

\frac{21 x + 7}{2 x} + 2

Schritte zur Lösung

\frac{d}{d x} ((x + 1) (7 x + 2))

Wende die Produktregel an:

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

f = x + 1, g = 7 x + 2

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

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

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

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

Vereinfache

1 \cdot (7 x + 2) + \frac{7}{2 x} (x + 1) : \frac{21 x + 7}{2 x} + 2

= \frac{21 x + 7}{2 x} + 2

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