derivative of (tan(x)^{-1})

Lösung

\frac{d}{d x} ((tan (x))^{- 1})

- csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} ((tan (x))^{- 1})

Wende die Kettenregel an:

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

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

\frac{d}{d x} (tan (x)) = sec^{2} (x)

= - \frac{1}{( tan ( x ) ) ^{2}} sec^{2} (x)

Vereinfache

- \frac{1}{tan ^{2} ( x )} sec^{2} (x) : - csc^{2} (x)

= - csc^{2} (x)

\int sec^{2} (x) tan^{4} (x) d x

x \to \infty lim (e^{\frac{- x}{100}})

x \to - 2 lim (\frac{x + 3}{x + 2})

t an g e n t (2 x^{2} + 2)^{3} (x^{2} - 1)^{2}

x \to 1 - lim (\frac{1}{x ^{3} - 1})