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Beliebt Rechnen >

derivative of \sqrt[3]{tan^2(x})

Lösung

\frac{d}{d x} (3 tan^{2} (x))

Lösung

\frac{2 sec ^{2} ( x )}{3 tan ^{\frac{1}{3}} ( x )}

Schritte zur Lösung

\frac{d}{d x} (3 tan^{2} (x))

Wende die Kettenregel an:

\frac{1}{3 ( tan ^{2} ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan^{2} (x))

= \frac{1}{3 ( tan ^{2} ( x ) ) ^{\frac{2}{3}}} \frac{d}{d x} (tan^{2} (x))

\frac{d}{d x} (tan^{2} (x)) = 2 tan (x) sec^{2} (x)

= \frac{1}{3 ( tan ^{2} ( x ) ) ^{\frac{2}{3}}} \cdot 2 tan (x) sec^{2} (x)

Vereinfache

\frac{1}{3 ( tan ^{2} ( x ) ) ^{\frac{2}{3}}} \cdot 2 tan (x) sec^{2} (x) : \frac{2 sec ^{2} ( x )}{3 tan ^{\frac{1}{3}} ( x )}

= \frac{2 sec ^{2} ( x )}{3 tan ^{\frac{1}{3}} ( x )}

Graph

Beliebte Beispiele

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\frac{d}{d x} (lo g_{n} (x))

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