derivative of 4cot(x/8)

Lösung

\frac{d}{d x} (4 cot (\frac{x}{8}))

- \frac{1}{2} csc^{2} (\frac{x}{8})

Schritte zur Lösung

\frac{d}{d x} (4 cot (\frac{x}{8}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{d}{d x} (cot (\frac{x}{8}))

Wende die Kettenregel an:

- csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

= - csc^{2} (\frac{x}{8}) \frac{d}{d x} (\frac{x}{8})

\frac{d}{d x} (\frac{x}{8}) = \frac{1}{8}

= 4 (- csc^{2} (\frac{x}{8}) \frac{1}{8})

Vereinfache

4 (- csc^{2} (\frac{x}{8}) \frac{1}{8}) : - \frac{1}{2} csc^{2} (\frac{x}{8})

= - \frac{1}{2} csc^{2} (\frac{x}{8})

in v erse l a pl a ce 0.5

\int (x^{6} + \frac{1}{1 - 4 x ^{2}}) d x

\int_{8}^{\infty} \frac{1}{x ^{2} + x} d x

y^{^{'}} = (y + 4 x)^{2}

x \to 1 + lim (\frac{x ^{2}}{x ^{2} - 1})