(\partial)/(\partial x)(3xe^{4xy})

Lösung

\frac{\partial}{\partial x} (3 x e^{4 x y})

3 (e^{4 x y} + 4 e^{4 x y} x y)

Schritte zur Lösung

\frac{\partial}{\partial x} (3 x e^{4 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= 3 \frac{\partial}{\partial x} (x e^{4 x y})

Wende die Produktregel an:

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

f = x, g = e^{4 x y}

= 3 (\frac{\partial}{\partial x} (x) e^{4 x y} + \frac{\partial}{\partial x} (e^{4 x y}) x)

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

\frac{\partial}{\partial x} (e^{4 x y}) = e^{4 x y} \cdot 4 y

= 3 (1 \cdot e^{4 x y} + e^{4 x y} \cdot 4 y x)

Vereinfache

= 3 (e^{4 x y} + 4 e^{4 x y} x y)

\int \frac{11 x}{x ^{2} + 1} d x

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