derivative of arcsinh(cot(x))

Lösung

\frac{d}{d x} (arcsinh (cot (x)))

- csc (x)

Schritte zur Lösung

\frac{d}{d x} (arcsinh (cot (x)))

Wende die Kettenregel an:

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

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

\frac{d}{d x} (cot (x)) = - csc^{2} (x)

= \frac{1}{( cot ( x ) ) ^{2} + 1} (- csc^{2} (x))

Vereinfache

\frac{1}{cot ^{2} ( x ) + 1} (- csc^{2} (x)) : - csc (x)

= - csc (x)

\frac{\partial}{\partial x} (y cos (z))

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

\int_{1}^{\infty} e^{- x} d x

\frac{\partial}{\partial y} (y^{2} - cos (x) y)

\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{3}{x ^{3}})