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Beliebt Rechnen >

derivative of ln((2x+1/(x-1)))

Lösung

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

Lösung

- \frac{3}{( 2 x + 1 ) ( x - 1 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

sum from n=1 to infinity of 7/((n+1)!)

n = 1 \sum \infty \frac{7}{( n + 1 ) !}

derivative of x^2sqrt(6x-7)

\frac{d}{d x} (x^{2} 6 x - 7)

tangent f(x)=1+5e^x,\at x=1

t an g e n t f (x) = 1 + 5 e^{x}, at x = 1

integral of (x+2)/(x^2(x-5))

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

xy+y^2+x^2-x^2y^'=0

x y + y^{2} + x^{2} - x^{2} y^{^{'}} = 0