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Popular >

derivative of e^{e^{e^x}}

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^{e^{e^x}} ?
The derivative of e^{e^{e^x}} is e^{e^{e^x}+e^x+x}
What is the first derivative of e^{e^{e^x}} ?
The first derivative of e^{e^{e^x}} is e^{e^{e^x}+e^x+x}