derivative of-4cot(xcsc(x))

Lösung

\frac{d}{d x} (- 4 cot (x) csc (x))

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

Schritte zur Lösung

\frac{d}{d x} (- 4 cot (x) csc (x))

Entferne die Konstante:

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

= - 4 \frac{d}{d x} (cot (x) csc (x))

Wende die Produktregel an:

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

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

= - 4 (\frac{d}{d x} (cot (x)) csc (x) + \frac{d}{d x} (csc (x)) cot (x))

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

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

= - 4 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x))

Vereinfache

- 4 ((- csc^{2} (x)) csc (x) + (- cot (x) csc (x)) cot (x)) : - 4 (csc (x) - 2 csc^{3} (x))

= - 4 (csc (x) - 2 csc^{3} (x))

\int - \frac{sin ( 8 x )}{8} d x

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