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Beliebt Rechnen >

derivative of (cos(x)/(sqrt(x)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of-3/(2t)

\int - \frac{3}{2 t} d t

inverselaplace s/((s-3)(s+1))

in v erse l a pl a ce \frac{s}{( s - 3 ) ( s + 1 )}

limit as x approaches infinity+of x^{-6}

x \to \infty + lim (x^{- 6})

taylor 11sin(-x)

t a y l or 11 sin (- x)

derivative of (2x+5/(3x-2))

\frac{d}{d x} (\frac{2 x + 5}{3 x - 2})