(\partial)/(\partial x)(7xe^{sqrt(xy)})

Lösung

\frac{\partial}{\partial x} (7 x e^{x y})

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

Schritte zur Lösung

\frac{\partial}{\partial x} (7 x e^{x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 7 \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}

= 7 (\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}

= 7 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x)

Vereinfache

7 (1 \cdot e^{x y} + \frac{y e ^{y x}}{2 x} x) : 7 (e^{x y} + \frac{e ^{x y} x y}{2})

= 7 (e^{x y} + \frac{e ^{x y} x y}{2})

\int_{0}^{3} 3 e^{- 2 x} d x

l a pl a ce t r an s f or m sin^{3} (t)

\int x 5^{- x^{2}} d x

d er i v a t i v e sec (x)

in v erse l a pl a ce \frac{1}{( s - 2 ) ( s + 1 )}