derivative of csc(xcot(x))

Lösung

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

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

Schritte zur Lösung

\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)

= \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)

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

Vereinfache

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

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

d er i v a t i v e x^{2}

a re a f (x) = - x^{2} + 2, g (x) = - x - 4

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