What is (\partial)/(\partial x)(e^{xe^x}) ?

The answer to (\partial)/(\partial x)(e^{xe^x}) is e^{xe^x}(e^x+e^xx)

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(\partial)/(\partial x)(e^{xe^x})

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

e^{x e^{x}} (e^{x} + e^{x} x)

Solution steps

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

Apply the chain rule:

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

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

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

= e^{x e^{x}} (e^{x} + e^{x} x)

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What is (\partial)/(\partial x)(e^{xe^x}) ?
The answer to (\partial)/(\partial x)(e^{xe^x}) is e^{xe^x}(e^x+e^xx)