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Beliebt Rechnen >

derivative of A(4e^{2x}x+4e^{2x})

Lösung

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

Lösung

A (8 e^{2 x} x + 12 e^{2 x})

Schritte zur Lösung

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

Entferne die Konstante:

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

= A \frac{d}{d x} (4 e^{2 x} x + 4 e^{2 x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= A (\frac{d}{d x} (4 e^{2 x} x) + \frac{d}{d x} (4 e^{2 x}))

\frac{d}{d x} (4 e^{2 x} x) = 4 (2 e^{2 x} x + e^{2 x})

\frac{d}{d x} (4 e^{2 x}) = 8 e^{2 x}

= A (4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x})

Multipliziere aus

4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x} : 8 e^{2 x} x + 12 e^{2 x}

= A (8 e^{2 x} x + 12 e^{2 x})

Graph

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