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Beliebt Rechnen >

derivative f(x)=-cot(x)csc(x)

Lösung

ableitung von

f (x) = - cot (x) csc (x)

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

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

= - \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)

= - (\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)

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

Vereinfache

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

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

Graph

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