(\partial)/(\partial x)(xe^{sqrt(15xy)})

Lösung

\frac{\partial}{\partial x} (x e^{15 x y})

\frac{15 e ^{15 x y} x y}{2} + e^{15 x y}

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{15 x y})

Vereinfache

x e^{15 x y} : e^{15 x y} x

= \frac{\partial}{\partial x} (e^{15 x y} x)

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = e^{15 x y}, g = x

= \frac{\partial}{\partial x} (e^{15 x y}) x + \frac{\partial}{\partial x} (x) e^{15 x y}

\frac{\partial}{\partial x} (e^{15 x y}) = \frac{15 y e ^{15 y x}}{2 x}

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

= \frac{15 y e ^{15 y x}}{2 x} x + 1 \cdot e^{15 x y}

Vereinfache

\frac{15 y e ^{15 y x}}{2 x} x + 1 \cdot e^{15 x y} : \frac{15 e ^{15 x y} x y}{2} + e^{15 x y}

= \frac{15 e ^{15 x y} x y}{2} + e^{15 x y}

\frac{\partial}{\partial x} (- y + x + 2)

n = 3 \sum \infty \frac{( - 1 ) ^{n + 1}}{n !}

\int e^{(x^{2})} d x

\int 3 e^{x^{2}} x d x

x \to 0 + lim (\frac{7 x}{∣ x ∣})