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Beliebt Rechnen >

derivative y=(x+9)(3sqrt(x)+4)

Lösung

ableitung von

y = (x + 9) (3 x + 4)

Lösung

\frac{9 x + 27}{2 x} + 4

Schritte zur Lösung

\frac{d}{d x} ((x + 9) (3 x + 4))

Wende die Produktregel an:

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

f = x + 9, g = 3 x + 4

= \frac{d}{d x} (x + 9) (3 x + 4) + \frac{d}{d x} (3 x + 4) (x + 9)

\frac{d}{d x} (x + 9) = 1

\frac{d}{d x} (3 x + 4) = \frac{3}{2 x}

= 1 \cdot (3 x + 4) + \frac{3}{2 x} (x + 9)

Vereinfache

1 \cdot (3 x + 4) + \frac{3}{2 x} (x + 9) : \frac{9 x + 27}{2 x} + 4

= \frac{9 x + 27}{2 x} + 4

Graph

Beliebte Beispiele

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