derivative of (2sin(x)/x)

Lösung

\frac{d}{d x} (\frac{2 sin ( x )}{x})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2 sin ( x )}{x})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

\frac{d x}{d x} = 1

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

Vereinfache

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

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

x \to 2 lim (\frac{x ^{2} - 4}{x ^{2} - 3 - 1})

\frac{\partial}{\partial z} (y z^{2})

\frac{\partial}{\partial x} (ln (x \cdot y))

t a y l or X^{\frac{9}{6}}, 8, 5

\int \frac{( 8 x - 3 )}{x ^{2} + x + 1} d x