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Beliebt Rechnen >

derivative y=sqrt(11+cot^2(x))

Lösung

ableitung von

y = 11 + cot^{2} (x)

Lösung

- \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (11 + cot^{2} (x))

Wende die Kettenregel an:

\frac{1}{2 11 + cot ^{2} ( x )} \frac{d}{d x} (11 + cot^{2} (x))

= \frac{1}{2 11 + cot ^{2} ( x )} \frac{d}{d x} (11 + cot^{2} (x))

\frac{d}{d x} (11 + cot^{2} (x)) = - 2 csc^{2} (x) cot (x)

= \frac{1}{2 11 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x))

Vereinfache

\frac{1}{2 11 + cot ^{2} ( x )} (- 2 csc^{2} (x) cot (x)) : - \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

= - \frac{csc ^{2} ( x ) cot ( x )}{11 + cot ^{2} ( x )}

Graph

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