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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

x \to 0 + lim (\frac{2 ^{x}}{3 ^{x}})

\int \frac{( x + 1 )}{x ^{2} + 2 x + 8} d x

\int x^{3} e^{x^{4 + 5}} d x

in v erse l a pl a ce \frac{4}{s \cdot ( s ^{2} - 4 s + 5 )}

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