(\partial)/(\partial x)(x^2y^2e^{6xy})

Lösung

\frac{\partial}{\partial x} (x^{2} y^{2} e^{6 x y})

y^{2} (2 x e^{6 x y} + e^{6 x y} \cdot 6 y x^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{2} e^{6 x y})

Behandle

y

als Konstante

Entferne die Konstante:

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

= y^{2} \frac{\partial}{\partial x} (x^{2} e^{6 x y})

Wende die Produktregel an:

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

f = x^{2}, g = e^{6 x y}

= y^{2} (\frac{\partial}{\partial x} (x^{2}) e^{6 x y} + \frac{\partial}{\partial x} (e^{6 x y}) x^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (e^{6 x y}) = e^{6 x y} \cdot 6 y

= y^{2} (2 x e^{6 x y} + e^{6 x y} \cdot 6 y x^{2})