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

Lösung

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

- \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

Schritte zur Lösung

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

Wende die Kettenregel an:

\frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} \frac{d}{d x} (sec (x) + tan (x))

= \frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} \frac{d}{d x} (sec (x) + tan (x))

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

= \frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} (- \frac{1}{- 1 + sin ( x )})

Vereinfache

\frac{1}{( sec ( x ) + tan ( x ) ) ^{2} + 1} (- \frac{1}{- 1 + sin ( x )}) : - \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

= - \frac{1}{( ( sec ( x ) + tan ( x ) ) ^{2} + 1 ) ( - 1 + sin ( x ) )}

\frac{d}{d x} (\frac{5}{x + 1})

d er i v a t i v e \frac{2}{1 + x ^{2}}

\int \frac{1}{x ^{2} + 12 x + 85} d x

d er i v a t i v e t e^{- 3 t}

\frac{d}{d x} (ln (x) csch (7 x))