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

Lösung

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

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

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

= 8 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x)

Vereinfache

8 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x) : 8 (e^{x y} + \frac{e ^{x y} x y}{2})

= 8 (e^{x y} + \frac{e ^{x y} x y}{2})

\frac{\partial}{\partial x} (\frac{( x - q )}{y} \cdot q)

\int_{1}^{16} x d x

in v erse l a pl a ce \frac{s}{s + 1.3}

\frac{\partial}{\partial x} (x y + \frac{x}{y})

d er i v a t i v e f (z) = e^{\frac{z}{z - 1}}