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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

(ln (x))^{'} = \frac{1}{x}

(x^{2})^{'} = 2 x

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

Vereinfache

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

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

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

d er i v a t i v e y = \frac{4 - x e ^{x}}{x + e ^{x}}

\int x^{2} \frac{1}{x} d x

\int_{4}^{7} \frac{1}{x ^{2} - 1} d x

\frac{d y}{d x} = 6 x + 2