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Beliebt Rechnen >

derivative derivative of 2sec^2(xtan(x))

Lösung

ableitung von

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

Lösung

- 4 sec^{2} (x) + 6 sec^{4} (x)

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec^{2} (x), g = tan (x)

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

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

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

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

Vereinfache

2 (2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x)) : - 4 sec^{2} (x) + 6 sec^{4} (x)

= - 4 sec^{2} (x) + 6 sec^{4} (x)

Graph

Beliebte Beispiele

derivative derivative of 6/x

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d er i v a t i v e \frac{d}{d x} (\frac{1}{( x ^{2} )})

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