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Beliebt Rechnen >

derivative (ln(x)+2)/(x^2)

Lösung

ableitung von

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

Lösung

\frac{- 2 ln ( x ) - 3}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of 1/(sqrt(-t^2+2t+3))

\int \frac{1}{- t ^{2} + 2 t + 3} d t

fläche 4x^2+y=4,x^8-y=1

a re a 4 x^{2} + y = 4, x^{8} - y = 1

integral from 1 to 5 of (sqrt(x-1))^2

\int_{1}^{5} (x - 1)^{2} d x

integral of (12)/(x^2)

\int \frac{12}{x ^{2}} d x

derivative of sqrt(x)-1/3 x

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