derivative of (ln(x)/(x^7))

Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{7}})

\frac{1 - 7 ln ( x )}{x ^{8}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{x ^{7}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) x ^{7} - \frac{d}{d x} ( x ^{7} ) ln ( x )}{( x ^{7} ) ^{2}}

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

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{\frac{1}{x} x ^{7} - 7 x ^{6} ln ( x )}{( x ^{7} ) ^{2}}

Vereinfache

\frac{\frac{1}{x} x ^{7} - 7 x ^{6} ln ( x )}{( x ^{7} ) ^{2}} : \frac{1 - 7 ln ( x )}{x ^{8}}

= \frac{1 - 7 ln ( x )}{x ^{8}}

\int_{1}^{3} 17 r^{3} ln (r) d r

y^{^{'}} - \frac{6 y}{x} = x^{6} e^{x}

\frac{d}{d y} (x y sin (y) + x y^{2} sin (x) + \frac{1}{x})

x \to 3 lim (csc (\frac{π x}{4}))

\int e^{- x} \cdot cos (x) d x