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Beliebt Rechnen >

derivative of (tan^2(x)/2)

Lösung

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

Lösung

sec^{2} (x) tan (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= sec^{2} (x) tan (x)

Graph

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