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Beliebt Rechnen >

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

Lösung

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

Lösung

sec (x)

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

Vereinfache

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

= sec (x)

Graph

Beliebte Beispiele

integral of 1200e^{0.3t}

\int 1200 e^{0.3 t} d t

integral from 0 to 1 of 1/(9+16x^2)

\int_{0}^{1} \frac{1}{9 + 16 x ^{2}} d x

maclaurin x/((3-x)^3)

ma c l a u r in \frac{x}{( 3 - x ) ^{3}}

integral from 0 to 7 of xe^{-x}

\int_{0}^{7} x e^{- x} d x

fläche x^2-1,-x+2,0,1

a re a x^{2} - 1, - x + 2, 0, 1