derivative of (sin(2x)/x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

\int sin^{2} (4 θ) d θ

l a pl a ce t r an s f or m f (t) = 5 cos (8 t) + 3 e^{- 4} sin (3 t)

\frac{d}{d x} ((x^{3} + 1)^{4})

\int sec (x) - cos (x) d x

d er i v a t i v e \frac{1}{2} ln (x)