derivative ln(1/(x^2))

Lösung

ableitung von

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

- \frac{2}{x}

Schritte zur Lösung

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

Vereinfache

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

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

- \frac{1}{x ^{2}} \cdot 2 x : - \frac{2}{x}

= - \frac{2}{x}

l a pl a ce t r an s f or m \frac{5}{3}

a re a x^{2}, 2 x - 1, 0

t a y l or \frac{1}{( 1 + x ) ^{\frac{1}{2}}}

\int \frac{1}{3 x ( 1 + 3 x )} d x

\int \frac{x + 2}{x - 2} (x^{2} - 4 x) d x