derivative of ((1-ln(x))/(x^2))

Lösung

\frac{d}{d x} (\frac{( 1 - ln ( x ) )}{x ^{2}})

- \frac{- 2 ln ( x ) + 3}{x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{( 1 - ln ( x ) )}{x ^{2}})

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Vereinfache

\frac{( - \frac{1}{x} ) x ^{2} - 2 x ( 1 - ln ( x ) )}{( x ^{2} ) ^{2}} : - \frac{- 2 ln ( x ) + 3}{x ^{3}}

= - \frac{- 2 ln ( x ) + 3}{x ^{3}}

t an g e n t f (x) = (x - 4) (x^{2} + 8), at x = 1

d er i v a t i v e (8 x + 9) (9 x - 10)

\frac{d}{d x} (e^{- c o s (x)})

d er i v a t i v e \frac{e ^{x}}{5 x + 3}

\int x^{2} sin (x^{3}) d x