derivative f(x)=(ln(x))/(13+x)

Lösung

ableitung von

f (x) = \frac{ln ( x )}{13 + x}

\frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{ln ( x )}{13 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ln ( x ) ) ( 13 + x ) - \frac{d}{d x} ( 13 + x ) ln ( x )}{( 13 + x ) ^{2}}

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

\frac{d}{d x} (13 + x) = 1

= \frac{\frac{1}{x} ( 13 + x ) - 1 \cdot ln ( x )}{( 13 + x ) ^{2}}

Vereinfache

\frac{\frac{1}{x} ( 13 + x ) - 1 \cdot ln ( x )}{( 13 + x ) ^{2}} : \frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

= \frac{13 + x - x ln ( x )}{x ( 13 + x ) ^{2}}

\int_{1}^{12} 2 x d x

\int \frac{9 e ^{2 t}}{1 + e ^{4 t}} d t

d er i v a t i v e f (x) = \frac{1}{2} x^{2} + 7 x

\int co tan (x) d x

x \to \frac{π}{3} lim (x cos (x))