(\partial)/(\partial x)(9xe^{sqrt(xy)})

Lösung

\frac{\partial}{\partial x} (9 x e^{x y})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (9 x e^{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \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}

= 9 (\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}

= 9 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x)

Vereinfache

9 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x) : 9 (e^{x y} + \frac{e ^{x y} x y}{2})

= 9 (e^{x y} + \frac{e ^{x y} x y}{2})

\frac{d}{d x} (arctan (\frac{3 x}{2}))

\int (tan (x))^{- 1} d x

\frac{\partial}{\partial x} (lo g_{10} (x))

x^{^{'}} = x - 4

\frac{d}{d x} (cos (x) + \frac{1}{x})