de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

\frac{d}{d x} (\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

y^{^{'}} = 2 x y + x

derivative of (2x-1^{3/2})

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

derivative e^{7x}(7x-1)^8

d er i v a t i v e e^{7 x} (7 x - 1)^{8}

sum from n=1 to infinity of 6/(sqrt(n))

n = 1 \sum \infty \frac{6}{n}

sum from n=1 to infinity of 1/(n^{7/2)}

n = 1 \sum \infty \frac{1}{n ^{\frac{7}{2}}}