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Beliebt Rechnen >

derivative of ln(cosh(4x))

Lösung

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

Lösung

4 tanh (4 x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (cosh (4 x)) = sinh (4 x) \cdot 4

= \frac{1}{cosh ( 4 x )} sinh (4 x) \cdot 4

Vereinfache

\frac{1}{cosh ( 4 x )} sinh (4 x) \cdot 4 : 4 tanh (4 x)

= 4 tanh (4 x)

Graph

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