derivative f(x)=5cot(x/8)

Lösung

ableitung von

f (x) = 5 cot (\frac{x}{8})

- \frac{5}{8} csc^{2} (\frac{x}{8})

Schritte zur Lösung

\frac{d}{d x} (5 cot (\frac{x}{8}))

Entferne die Konstante:

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

= 5 \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}

= 5 (- csc^{2} (\frac{x}{8}) \frac{1}{8})

Vereinfache

5 (- csc^{2} (\frac{x}{8}) \frac{1}{8}) : - \frac{5}{8} csc^{2} (\frac{x}{8})

= - \frac{5}{8} csc^{2} (\frac{x}{8})

x \to 0 lim (x^{5} ln (x))

\frac{d}{d y} (x^{y^{2}})

\int (3 x^{2} + 10 x) (x^{3} + 5 x^{2} + 6) d x

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

x \to 0 lim (\frac{0}{x ^{3}})