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Beliebt Rechnen >

derivative of (sin(x)/(sqrt(x)))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

integral of xcos(x^2+5)

\int x cos (x^{2} + 5) d x

integral of (y-3)/(y-2)

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

y^{^{'}} = (x + y)^{2} - 1

tan(f(x))(x)=-4x+1/2 x-5,\at x=1

tan (f (x)) (x) = - 4 x + \frac{1}{2} x - 5, at x = 1

(\partial)/(\partial x)(3x^{2y})

\frac{\partial}{\partial x} (3 x^{2 y})