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Beliebt Rechnen >

derivative of 2xe^y

Lösung

\frac{d}{d x} (2 x e^{y})

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (2 x e^{y})

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = e^{y}

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

\frac{d x}{d x} = 1

\frac{d}{d x} (e^{y}) = e^{y} \frac{d y}{d x}

= 2 (1 \cdot e^{y} + e^{y} \frac{d y}{d x} x)

Vereinfache

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

Beliebte Beispiele

\int - 4 d x

(\partial)/(\partial y)(3x-4y)

\frac{\partial}{\partial y} (3 x - 4 y)

integral of e^xcos(nx)

\int e^{x} cos (n x) d x

integral of 7sin^2(xco)s^3x

\int 7 sin^{2} (x co) s^{3} x d x

integral from-3 to 3 of (12)/(x^2-2x-35)

\int_{- 3}^{3} \frac{12}{x ^{2} - 2 x - 35} d x