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Beliebt Rechnen >

(\partial)/(\partial x)(2ye^{4x^2-6y})

Lösung

\frac{\partial}{\partial x} (2 y e^{4 x^{2} - 6 y})

Lösung

16 e^{4 x^{2} - 6 y} y x

Schritte zur Lösung

\frac{\partial}{\partial x} (2 y e^{4 x^{2} - 6 y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 2 y \frac{\partial}{\partial x} (e^{4 x^{2} - 6 y})

Wende die Kettenregel an:

e^{4 x^{2} - 6 y} \frac{\partial}{\partial x} (4 x^{2} - 6 y)

= e^{4 x^{2} - 6 y} \frac{\partial}{\partial x} (4 x^{2} - 6 y)

\frac{\partial}{\partial x} (4 x^{2} - 6 y) = 8 x

= 2 y e^{4 x^{2} - 6 y} \cdot 8 x

Vereinfache

= 16 e^{4 x^{2} - 6 y} y x

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