derivative (ln(x))/(x^9)

Lösung

ableitung von

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

\frac{1 - 9 ln ( x )}{x ^{10}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{9}) = 9 x^{8}

= \frac{\frac{1}{x} x ^{9} - 9 x ^{8} ln ( x )}{( x ^{9} ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x ^{9} - 9 x ^{8} ln ( x )}{( x ^{9} ) ^{2}} : \frac{1 - 9 ln ( x )}{x ^{10}}

= \frac{1 - 9 ln ( x )}{x ^{10}}

d er i v a t i v e 4 e^{6 x} + 2 x

t an g e n t f (x) = 32 - x, at x = 7

d er i v a t i v e 4 x^{3}

\frac{d}{d t} (\frac{3}{t})

\frac{d}{d x} (2 arctan (sin (x)))