de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative (ln(x))/(x^3)

Lösung

ableitung von

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

Lösung

\frac{1 - 3 ln ( x )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{3}})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{\frac{1}{x} x ^{3} - 3 x ^{2} ln ( x )}{( x ^{3} ) ^{2}} : \frac{1 - 3 ln ( x )}{x ^{4}}

= \frac{1 - 3 ln ( x )}{x ^{4}}

Graph

Beliebte Beispiele

(\partial)/(\partial x)(cos(x/2))

derivative f(x)=(x^{12})/(x^2)

derivative (8x)/(x^2+1)

derivative of 2(x^2+y^2^2)

integral of cos(3x)cos(9x)