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Beliebt Rechnen >

derivative ln(tan(4x))

Lösung

ableitung von

ln (tan (4 x))

Lösung

4 sec^{2} (4 x) cot (4 x)

Schritte zur Lösung

\frac{d}{d x} (ln (tan (4 x)))

Wende die Kettenregel an:

\frac{1}{tan ( 4 x )} \frac{d}{d x} (tan (4 x))

= \frac{1}{tan ( 4 x )} \frac{d}{d x} (tan (4 x))

\frac{d}{d x} (tan (4 x)) = sec^{2} (4 x) \cdot 4

= \frac{1}{tan ( 4 x )} sec^{2} (4 x) \cdot 4

Vereinfache

\frac{1}{tan ( 4 x )} sec^{2} (4 x) \cdot 4 : 4 sec^{2} (4 x) cot (4 x)

= 4 sec^{2} (4 x) cot (4 x)

Graph

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