derivative (2(1-ln(x)))/(x^2)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to - 2 lim (3 x^{2} + 5 x - 1)

\int \frac{t}{( t ^{2} + 1 ) ^{\frac{5}{2}}} d t

\int \frac{1}{16 x ^{2} + 7} d x

d er i v a t i v e \frac{13}{x}

\frac{d}{d t} (e^{7 t s i n (2 t)})