derivative of (sin(3x)/x)

Lösung

\frac{d}{d x} (\frac{sin ( 3 x )}{x})

\frac{3 x cos ( 3 x ) - sin ( 3 x )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( 3 x )}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( sin ( 3 x ) ) x - \frac{d x}{d x} sin ( 3 x )}{x ^{2}}

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

= \frac{cos ( 3 x ) \cdot 3 x - 1 \cdot sin ( 3 x )}{x ^{2}}

Vereinfache

= \frac{3 x cos ( 3 x ) - sin ( 3 x )}{x ^{2}}

6 y^{^{''}} + 8 y^{^{'}} + y = 0, y (- 2) = - 3, y^{^{'}} (- 2) = - 4

x \to 4 lim (- \frac{15}{x - 4})

\frac{\partial}{\partial x} (sin (π x))

\frac{d}{d x} (4 x^{5})

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{5 x}