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Beliebt Rechnen >

derivative of ln(1-3/x)

Lösung

\frac{d}{d x} (ln (1 - \frac{3}{x}))

Lösung

\frac{3}{x ( x - 3 )}

Schritte zur Lösung

\frac{d}{d x} (ln (1 - \frac{3}{x}))

Wende die Kettenregel an:

\frac{1}{1 - \frac{3}{x}} \frac{d}{d x} (1 - \frac{3}{x})

= \frac{1}{1 - \frac{3}{x}} \frac{d}{d x} (1 - \frac{3}{x})

\frac{d}{d x} (1 - \frac{3}{x}) = \frac{3}{x ^{2}}

= \frac{1}{1 - \frac{3}{x}} \cdot \frac{3}{x ^{2}}

Vereinfache

\frac{1}{1 - \frac{3}{x}} \cdot \frac{3}{x ^{2}} : \frac{3}{x ( x - 3 )}

= \frac{3}{x ( x - 3 )}

Graph

Beliebte Beispiele

limit as x approaches 2 of (x^2-2x)/x

x \to 2 lim (\frac{x ^{2} - 2 x}{x})

integral of 2/(x^3)

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

integral of ((3x^2+6))/((x^2-2x+2)^2)

\int \frac{( 3 x ^{2} + 6 )}{( x ^{2} - 2 x + 2 ) ^{2}} d x

derivative of (3x+1ln(x-1))

\frac{d}{d x} ((3 x + 1) ln (x - 1))

derivative of (4x-7^3)

\frac{d}{d x} ((4 x - 7)^{3})