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Beliebt Rechnen >

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

Lösung

ableitung von

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

Lösung

\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}}

Graph

Beliebte Beispiele

integral of 1/2 ln(x)

\int \frac{1}{2} ln (x) d x

derivative of-8e^{-x}

\frac{d}{d x} (- 8 e^{- x})

4x^{''}+2x^'+4x=100,x(0)=5,x^'(0)=0

4 x^{^{''}} + 2 x^{^{'}} + 4 x = 100, x (0) = 5, x^{^{'}} (0) = 0

limit as x approaches 3 of sqrt(5x^2+2x)

x \to 3 lim (5 x^{2} + 2 x)

x*(dy)/(dx)+y=e^{-x}

x \cdot \frac{d y}{d x} + y = e^{- x}