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

Lösung

ableitung von

\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}}

θ \to 0 lim (\frac{sin ( 7 θ )}{θ})

d er i v a t i v e x^{2} - 5 x + 9

d er i v a t i v e y = arccos (4 x^{4})

\frac{\partial}{\partial x} (\frac{x}{x ^{2} - 2 x + 1})

\frac{d}{d x} (ln (\frac{x + 1}{x - 1}))