derivative of (ln(x)/(9x))

Lösung

\frac{d}{d x} (\frac{ln ( x )}{9 x})

\frac{1 - ln ( x )}{9 x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{9 x})

Entferne die Konstante:

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

= \frac{1}{9} \frac{d}{d x} (\frac{ln ( x )}{x})

Wende die Quotientenregel an:

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

= \frac{1}{9} \cdot \frac{\frac{d}{d x} ( ln ( x ) ) x - \frac{d x}{d x} ln ( x )}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{1}{9} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}}

Vereinfache

\frac{1}{9} \cdot \frac{\frac{1}{x} x - 1 \cdot ln ( x )}{x ^{2}} : \frac{1 - ln ( x )}{9 x ^{2}}

= \frac{1 - ln ( x )}{9 x ^{2}}

\int (\frac{1}{e ^{3 t}}) d t

x \to 0 lim (\frac{e - 1}{x})

\frac{d}{d x} (x^{4} - 3 x^{2} + 3)

x \to 1 lim (\frac{∣ 3 - x ∣}{3 - x})

\frac{d}{d x} (\frac{x ^{2}}{5 + x})