((ln^2(x))/x)^'

Lösung

(\frac{ln ^{2} ( x )}{x})^{^{'}}

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

Schritte zur Lösung

(\frac{ln ^{2} ( x )}{x})^{'}

Wende die Quotientenregel an:

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

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

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

x^{'} = 1

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

Vereinfache

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

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

x \to 2 lim (cos (x - 2))

x \to \infty lim (1 + \frac{x}{2})

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

\frac{\partial}{\partial y} (e^{2 x + y})

\frac{d}{d y} (3 x^{2} y + e^{y})