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Beliebt Rechnen >

(\partial)/(\partial x)(3sec^2(2x+3y))

Lösung

\frac{\partial}{\partial x} (3 sec^{2} (2 x + 3 y))

Lösung

12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

Schritte zur Lösung

\frac{\partial}{\partial x} (3 sec^{2} (2 x + 3 y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (sec^{2} (2 x + 3 y))

Wende die Kettenregel an:

2 sec (2 x + 3 y) \frac{\partial}{\partial x} (sec (2 x + 3 y))

= 2 sec (2 x + 3 y) \frac{\partial}{\partial x} (sec (2 x + 3 y))

\frac{\partial}{\partial x} (sec (2 x + 3 y)) = sec (2 x + 3 y) tan (2 x + 3 y) \cdot 2

= 3 \cdot 2 sec (2 x + 3 y) sec (2 x + 3 y) tan (2 x + 3 y) \cdot 2

Vereinfache

3 \cdot 2 sec (2 x + 3 y) sec (2 x + 3 y) tan (2 x + 3 y) \cdot 2 : 12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

= 12 sec^{2} (2 x + 3 y) tan (2 x + 3 y)

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