derivative of (ln(x)/(5ln(x)+4))

Lösung

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})

\frac{4}{x ( 5 ln ( x ) + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{5 ln ( x ) + 4})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) ( 5 ln ( x ) + 4 ) - \frac{d}{d x} ( 5 ln ( x ) + 4 ) ln ( x )}{( 5 ln ( x ) + 4 ) ^{2}}

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

\frac{d}{d x} (5 ln (x) + 4) = \frac{5}{x}

= \frac{\frac{1}{x} ( 5 ln ( x ) + 4 ) - \frac{5}{x} ln ( x )}{( 5 ln ( x ) + 4 ) ^{2}}

Vereinfache

\frac{\frac{1}{x} ( 5 ln ( x ) + 4 ) - \frac{5}{x} ln ( x )}{( 5 ln ( x ) + 4 ) ^{2}} : \frac{4}{x ( 5 ln ( x ) + 4 ) ^{2}}

= \frac{4}{x ( 5 ln ( x ) + 4 ) ^{2}}

\int_{1}^{4} t ln (t) d t

s l o p e y = x + 3 y = x + 1 y = - x + 1

\frac{d}{d x} (\frac{3 x + 2}{x - 1})

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

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