derivative y=(ln(x))/(x^5)

Lösung

ableitung von

y = \frac{ln ( x )}{x ^{5}}

\frac{1 - 5 ln ( x )}{x ^{6}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{5} - \frac{d}{d x} ( x ^{5} ) ln ( x )}{( x ^{5} ) ^{2}}

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

= \frac{\frac{1}{x} x ^{5} - 5 x ^{4} ln ( x )}{( x ^{5} ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x ^{5} - 5 x ^{4} ln ( x )}{( x ^{5} ) ^{2}} : \frac{1 - 5 ln ( x )}{x ^{6}}

= \frac{1 - 5 ln ( x )}{x ^{6}}

\int \frac{e ^{3 t}}{t} d t

\int in (x) d x

n = 1 \sum \infty \frac{1}{( 2 n - 1 ) ^{5}}

\frac{d}{d x} (4 x^{5} - 5 x^{4})

t an g e n t x^{3} + y^{3} - 6 x y = 0, (\frac{4}{3}, \frac{8}{3})