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Beliebt Rechnen >

derivative of cot^4(x-csc^4(x))

Lösung

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

Lösung

4 csc^{2} (x) cot (x)

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (cot^{4} (x)) = - 4 cot^{3} (x) csc^{2} (x)

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

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

Vereinfache

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

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

Graph

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