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Beliebt Rechnen >

((sin(x))/x)^'

Lösung

(\frac{sin ( x )}{x})^{^{'}}

Lösung

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

Schritte zur Lösung

(\frac{sin ( x )}{x})^{'}

Wende die Quotientenregel an:

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

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

(sin (x))^{'} = cos (x)

x^{'} = 1

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

Vereinfache

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

Graph

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