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

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

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

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

e^{e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{e^{x}} e^{x}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{x}} e^{x} = e^{e^{x} + x}

= e^{e^{x} + x}

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