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Beliebt Rechnen >

derivative of sqrt(x)ln(2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = ln (2 x)

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

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

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

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

Vereinfache

\frac{1}{2 x} ln (2 x) + \frac{1}{x} x : \frac{ln ( 2 x )}{2 x} + \frac{1}{x}

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

Graph

Beliebte Beispiele

limit as x approaches 2+of x^2

x \to 2 + lim (x^{2})

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integral of (2x)/(sqrt(2x+1))

\int \frac{2 x}{2 x + 1} d x

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x y^{2} + 1 + x^{2} \frac{d y}{d x} = 0

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