derivative of 2csc(xcot(x))

Lösung

\frac{d}{d x} (2 csc (x) cot (x))

2 (csc (x) - 2 csc^{3} (x))

Schritte zur Lösung

\frac{d}{d x} (2 csc (x) cot (x))

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = csc (x), g = cot (x)

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

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

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

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

Vereinfache

2 ((- cot (x) csc (x)) cot (x) + (- csc^{2} (x)) csc (x)) : 2 (csc (x) - 2 csc^{3} (x))

= 2 (csc (x) - 2 csc^{3} (x))

t an g e n t y = 2 x + 1, at x = \frac{1}{4}

in v erse l a pl a ce \frac{s ^{2}}{( s - 3 ) ( s ^{2} + 5 )}

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

\frac{\partial}{\partial z} (2 x z^{3} e^{y^{2}})

\int_{5}^{9} x^{2} d x