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Beliebt Rechnen >

derivative f(x)=(x+sqrt(2)x)(2x+1)

Lösung

ableitung von

f (x) = (x + 2 x) (2 x + 1)

Lösung

4 x + 42 x + 1 + 2

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

= (1 + 2) (2 x + 1) + 2 (x + 2 x)

Vereinfache

(1 + 2) (2 x + 1) + 2 (x + 2 x) : 4 x + 42 x + 1 + 2

= 4 x + 42 x + 1 + 2

Graph

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