derivative of e^{arccsc(x})

Lösung

\frac{d}{d x} (e^{arccsc (x)})

- \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

Schritte zur Lösung

\frac{d}{d x} (e^{arccsc (x)})

Wende die Kettenregel an:

e^{arccsc (x)} \frac{d}{d x} (arccsc (x))

= e^{arccsc (x)} \frac{d}{d x} (arccsc (x))

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

= e^{arccsc (x)} (- \frac{1}{x ^{2} x ^{2} - 1})

Vereinfache

e^{arccsc (x)} (- \frac{1}{x ^{2} x ^{2} - 1}) : - \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

= - \frac{e ^{arccsc (x)}}{x x ^{2} - 1}

f (x) = 4 x

\frac{\partial}{\partial x} (- 15 (3 x + y)^{4})

y^{^{'}} = (y - 1)^{2}

\frac{d}{d x} (- \frac{4 x}{( x ^{2} - 4 ) ^{2}})

\frac{d}{d x} ((\frac{x ^{2} + 6}{x ^{2} - 6})^{3})