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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (e^{\frac{1}{f ( x )}})

\int \frac{1}{5 ^{x}} d x

\frac{d y}{d x} + 2 x y = 2 x

in v erse l a pl a ce \frac{1}{s ^{2} - 3 s + 5}

y^{^{'}} = \frac{( 4 t ^{3} + 1 )}{( 2 y - 6 )}