(\partial)/(\partial x)(8xe^{xy})

Lösung

\frac{\partial}{\partial x} (8 x e^{x y})

8 (e^{x y} + e^{x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (8 x e^{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 8 \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}

= 8 (\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}) = e^{x y} y

= 8 (1 \cdot e^{x y} + e^{x y} y x)

Vereinfache

= 8 (e^{x y} + e^{x y} x y)

n = 1 \sum \infty \frac{n !}{n 2 ^{n}}

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

\int x^{2} - 4 x + 7 d x

x \to - 1 lim (\frac{x ^{2} - 3}{1 - x})

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