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Beliebt Rechnen >

derivative of (sin(5x)/x)

Lösung

\frac{d}{d x} (\frac{sin ( 5 x )}{x})

Lösung

\frac{5 x cos ( 5 x ) - sin ( 5 x )}{x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( 5 x )}{x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( sin ( 5 x ) ) x - \frac{d x}{d x} sin ( 5 x )}{x ^{2}}

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

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

= \frac{cos ( 5 x ) \cdot 5 x - 1 \cdot sin ( 5 x )}{x ^{2}}

Vereinfache

= \frac{5 x cos ( 5 x ) - sin ( 5 x )}{x ^{2}}

Graph

Beliebte Beispiele

((cos (x))^{2})^{^{'}}

integral of x^5ln(3x)

\int x^{5} ln (3 x) d x

integral of 3x^2+4

\int 3 x^{2} + 4 d x

limit as x approaches 3 of sqrt(x^2+7)+5

x \to 3 lim (x^{2} + 7 + 5)

derivative y=4x^3sqrt(1-x^2)

d er i v a t i v e y = 4 x^{3} 1 - x^{2}