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Beliebt Rechnen >

(\partial)/(\partial x)(2xe^{sqrt(xy)})

Lösung

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

Lösung

2 e^{x y} + e^{x y} x y

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

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

f = x, g = e^{x y}

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

= 2 e^{x y} + e^{x y} x y

Beliebte Beispiele

limit as x approaches 6 of (3x)/(x^2-6x)

x \to 6 lim (\frac{3 x}{x ^{2} - 6 x})

integral from 1 to infinity of sqrt(x)

\int_{1}^{\infty} x d x

(dy)/(dx)= y/x+3x+7

\frac{d y}{d x} = \frac{y}{x} + 3 x + 7

faktorisieren 3x^4-12x^3

f a c t or 3 x^{4} - 12 x^{3}

derivative of sin^5(x/3)

\frac{d}{d x} (sin^{5} (\frac{x}{3}))