derivative of (x+2/(ln(x)))

Lösung

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x + 2}{ln ( x )})

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

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

so l v e f or x, \frac{d ^{2} x}{d t ^{2}} + x = (t^{2} + t) sin (t)

s l o p e (- 5, 11), (- 10, 6)

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