derivative-csc(x)cot(x)

Lösung

ableitung von

- csc (x) cot (x)

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= - \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)

10 x + \frac{d y}{d x} = 0

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