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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

4 x + 32 x + \frac{1}{2 x} + 1

Schritte zur Lösung

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

Vereinfache

(x + 2 x) (2 x + 1) : (x + 2 x) (2 x + 1)

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

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

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

Vereinfache

(1 + \frac{1}{2 x}) (2 x + 1) + 2 (x + 2 x) : 4 x + 32 x + \frac{1}{2 x} + 1

= 4 x + 32 x + \frac{1}{2 x} + 1

Graph

Beliebte Beispiele

integral of 20-3sqrt(16-2x)

\int 20 - 3 16 - 2 x d x

fläche y=3x,y=x^2

a re a y = 3 x, y = x^{2}

taylor e^xln(1+x)

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limit as x approaches 4 of (3-x)/(x-4)

x \to 4 lim (\frac{3 - x}{x - 4})

limit as x approaches 0 of 2x+c

x \to 0 lim (2 x + c)