derivative of (sin(x)/(ln(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Vereinfache

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

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

\frac{d}{d x} (arctan (2 x^{2} - 4))

y^{^{''}} - 8 y^{^{'}} + 16 = 0

x \to π lim ((π - x) cot (x))

l a pl a ce t r an s f or m (e^{- 1}) (sin (2 t))

d er i v a t i v e e^{8 x} cos (11 x)