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Beliebt Rechnen >

derivative of ln(sin(3x))

Lösung

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

Lösung

3 cot (3 x)

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{sin ( 3 x )} \frac{d}{d x} (sin (3 x))

= \frac{1}{sin ( 3 x )} \frac{d}{d x} (sin (3 x))

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

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

Vereinfache

\frac{1}{sin ( 3 x )} cos (3 x) \cdot 3 : 3 cot (3 x)

= 3 cot (3 x)

Graph

Beliebte Beispiele

derivative of x^{2/3}-x^{1/3}+4

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

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integral of xe^{12x}

\int x e^{12 x} d x

(\partial)/(\partial x)(-4sqrt(x))

\frac{\partial}{\partial x} (- 4 x)

integral of 1/(sqrt(2x-5))

\int \frac{1}{2 x - 5} d x