derivative of ln(arcsin(cos(x)))

Lösung

\frac{d}{d x} (ln (arcsin (cos (x))))

- \frac{1}{arcsin ( cos ( x ) )}

Schritte zur Lösung

\frac{d}{d x} (ln (arcsin (cos (x))))

Wende die Kettenregel an:

\frac{1}{arcsin ( cos ( x ) )} \frac{d}{d x} (arcsin (cos (x)))

= \frac{1}{arcsin ( cos ( x ) )} \frac{d}{d x} (arcsin (cos (x)))

\frac{d}{d x} (arcsin (cos (x))) = - csc (x) sin^{2} (x)

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

Vereinfache

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

= - \frac{1}{arcsin ( cos ( x ) )}

\frac{d y}{d x} + 4 y = 11

\int \frac{( x ^{2} - 1 )}{x ^{\frac{3}{2}}} d x

\frac{d}{d x} (a - x)

\int x 6^{x} d x

x \to 9 + lim (\frac{5 x}{x - 9})