derivative (ln(x))/(sqrt(x))

Lösung

ableitung von

\frac{ln ( x )}{x}

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

Vereinfache

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

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

\int_{0}^{1} x 3 1 - x d x

\int \frac{1}{( 1 + e ^{- x} )} d x

\frac{\partial}{\partial x} (sin (\frac{x}{2}))

\int_{1}^{4} x^{2} - 2 x + 3 d x

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