(\partial)/(\partial x)(3ax^2+e^{xx}+e^x)

Lösung

\frac{\partial}{\partial x} (3 a x^{2} + e^{xx} + e^{x})

6 a x + e^{x^{2}} \cdot 2 x + e^{x}

Schritte zur Lösung

\frac{\partial}{\partial x} (3 a x^{2} + e^{xx} + e^{x})

Vereinfache

3 a x^{2} + e^{xx} + e^{x} : 3 a x^{2} + e^{x^{2}} + e^{x}

= \frac{\partial}{\partial x} (3 a x^{2} + e^{x^{2}} + e^{x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (3 a x^{2}) + \frac{\partial}{\partial x} (e^{x^{2}}) + \frac{\partial}{\partial x} (e^{x})

\frac{\partial}{\partial x} (3 a x^{2}) = 6 a x

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

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

= 6 a x + e^{x^{2}} \cdot 2 x + e^{x}