What is (\partial)/(\partial x)(3ax^2+e^xx+e^x) ?

The answer to (\partial)/(\partial x)(3ax^2+e^xx+e^x) is 6ax+e^xx+2e^x

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= 6 a x + e^{x} x + e^{x} + e^{x}

Simplify

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

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What is (\partial)/(\partial x)(3ax^2+e^xx+e^x) ?
The answer to (\partial)/(\partial x)(3ax^2+e^xx+e^x) is 6ax+e^xx+2e^x