derivative of xcsc(x-cot(x))

Lösung

\frac{d}{d x} (x csc (x) - cot (x))

csc (x) - x cot (x) csc (x) + csc^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (x csc (x) - cot (x))

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= csc (x) - x cot (x) csc (x) - (- csc^{2} (x))

Vereinfache

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

n = 0 \sum \infty \frac{6}{2 ^{n}}

d er i v a t i v e f (x) = \frac{- 6}{x}

\frac{\partial}{\partial x} (- 8 x y - 2 x^{4} - 2 y^{4})

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})

d er i v a t i v e f (x) = \frac{x - 3}{x + 3}