derivative of ln|sec(x|)

Lösung

\frac{d}{d x} (ln ∣ sec (x) ∣)

tan (x)

Schritte zur Lösung

\frac{d}{d x} (ln ∣ sec (x) ∣)

Wende die Kettenregel an:

\frac{1}{∣ sec ( x ) ∣} \frac{d}{d x} (∣ sec (x) ∣)

= \frac{1}{∣ sec ( x ) ∣} \frac{d}{d x} (∣ sec (x) ∣)

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

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

Vereinfache

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

= tan (x)