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Beliebt Rechnen >

derivative of (sin(3x)/(cos(2x)))

Lösung

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 2 x )})

Lösung

cos (3 x) \cdot 3 sec (2 x) + sec (2 x) tan (2 x) \cdot 2 sin (3 x)

Schritte zur Lösung

\frac{d}{d x} (\frac{sin ( 3 x )}{cos ( 2 x )})

Vereinfache

\frac{sin ( 3 x )}{cos ( 2 x )} : sin (3 x) sec (2 x)

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (3 x), g = sec (2 x)

= \frac{d}{d x} (sin (3 x)) sec (2 x) + \frac{d}{d x} (sec (2 x)) sin (3 x)

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

\frac{d}{d x} (sec (2 x)) = sec (2 x) tan (2 x) \cdot 2

= cos (3 x) \cdot 3 sec (2 x) + sec (2 x) tan (2 x) \cdot 2 sin (3 x)

Graph

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