derivative of (d/(dx(ln(x)))/x)

Lösung

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

- \frac{1}{x ^{3}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

\frac{d ^{2} x}{d x ^{2}} = 0

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

= \frac{( - \frac{1}{x ^{2}} ) x - 0 \cdot \frac{1}{x}}{x ^{2}}

Vereinfache

\frac{( - \frac{1}{x ^{2}} ) x - 0 \cdot \frac{1}{x}}{x ^{2}} : - \frac{1}{x ^{3}}

= - \frac{1}{x ^{3}}

a re a x^{2}, 8 + x

d er i v a t i v e f (x) = - 3 e^{- 5 x}

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

d er i v a t i v e cos^{9} (x)

x \to - 5 + lim (25 - x^{2})