derivative of 3sec^2(pix-1)

Lösung

\frac{d}{d x} (3 sec^{2} (π x - 1))

6 π sec^{2} (π x - 1) tan (π x - 1)

Schritte zur Lösung

\frac{d}{d x} (3 sec^{2} (π x - 1))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (sec^{2} (π x - 1))

Wende die Kettenregel an:

2 sec (π x - 1) \frac{d}{d x} (sec (π x - 1))

= 2 sec (π x - 1) \frac{d}{d x} (sec (π x - 1))

\frac{d}{d x} (sec (π x - 1)) = sec (π x - 1) tan (π x - 1) π

= 3 \cdot 2 sec (π x - 1) sec (π x - 1) tan (π x - 1) π

Vereinfache

3 \cdot 2 sec (π x - 1) sec (π x - 1) tan (π x - 1) π : 6 π sec^{2} (π x - 1) tan (π x - 1)

= 6 π sec^{2} (π x - 1) tan (π x - 1)

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