derivative arcsin(sin(x))

Lösung

ableitung von

arcsin (sin (x))

sec (x) cos^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (arcsin (sin (x)))

Wende die Kettenregel an:

\frac{1}{1 - ( sin ( x ) ) ^{2}} \frac{d}{d x} (sin (x))

= \frac{1}{1 - ( sin ( x ) ) ^{2}} \frac{d}{d x} (sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

= \frac{1}{1 - ( sin ( x ) ) ^{2}} cos (x)

Vereinfache

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

= sec (x) cos^{2} (x)

\frac{d}{d x} (\frac{1}{x ln ( 10 )})

d er i v a t i v e f (x) = \frac{1 + e ^{x}}{1 - e ^{x}}

\frac{d y}{d x} = e^{(3 x + 2 y)}

t an g e n t f (x) = x^{2} + 3 x, at x = 1

\frac{d}{d x} (4 - \frac{15}{4 x ^{\frac{1}{4}}})