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Beliebt Rechnen >

derivative of ln(x/k)

Lösung

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

Lösung

\frac{1}{x}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{\frac{x}{k}} \frac{d}{d x} (\frac{x}{k})

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

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

= \frac{1}{\frac{x}{k}} \cdot \frac{1}{k}

Vereinfache

\frac{1}{\frac{x}{k}} \cdot \frac{1}{k} : \frac{1}{x}

= \frac{1}{x}

Graph

Beliebte Beispiele

integral from-a to a of 1/((s-x)^2)

\int_{- a}^{a} \frac{1}{( s - x ) ^{2}} d x

derivative of (x^2-4/(x^2-2x))

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 2 x})

integral of 2/(x^{2/3)}

\int \frac{2}{x ^{\frac{2}{3}}} d x

2y*(dy)/(dx)=x(y^2+1)

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

derivative of in(x^2-5)

\frac{d}{d x} (in (x^{2} - 5))