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Beliebt Rechnen >

derivative of ln(tan(x+sec(x)))

Lösung

\frac{d}{d x} (ln (tan (x) + sec (x)))

Lösung

sec (x)

Schritte zur Lösung

\frac{d}{d x} (ln (tan (x) + sec (x)))

Wende die Kettenregel an:

\frac{1}{tan ( x ) + sec ( x )} \frac{d}{d x} (tan (x) + sec (x))

= \frac{1}{tan ( x ) + sec ( x )} \frac{d}{d x} (tan (x) + sec (x))

\frac{d}{d x} (tan (x) + sec (x)) = - \frac{1}{- 1 + sin ( x )}

= \frac{1}{tan ( x ) + sec ( x )} (- \frac{1}{- 1 + sin ( x )})

Vereinfache

\frac{1}{tan ( x ) + sec ( x )} (- \frac{1}{- 1 + sin ( x )}) : sec (x)

= sec (x)

Graph

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