derivative (ln(x))/(5x^2)

Lösung

ableitung von

\frac{ln ( x )}{5 x ^{2}}

\frac{1 - 2 ln ( x )}{5 x ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{5 x ^{2}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{5} \frac{d}{d x} (\frac{ln ( x )}{x ^{2}})

Wende die Quotientenregel an:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( ln ( x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ln ( x )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{5} \cdot \frac{\frac{1}{x} x ^{2} - 2 x ln ( x )}{( x ^{2} ) ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{\frac{1}{x} x ^{2} - 2 x ln ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{5 x ^{3}}

= \frac{1 - 2 ln ( x )}{5 x ^{3}}

\frac{\partial}{\partial x} (e^{2 x + 7 y})

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

d er i v a t i v e f (x) = 4 sec (4 x)

\int (6 x^{5} + 7) x^{6} + 7 x d x

d er i v a t i v e lo g_{e} (sec (\frac{1}{5 x}))