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derivative of e^{(e^{x^2}})

Solution

\frac{d}{d x} (e^{(e^{x^{2}})})

Solution

2 e^{e^{x^{2}} + x^{2}} x

Solution steps

\frac{d}{d x} (e^{(e^{x^{2}})})

Apply the chain rule:

e^{e^{x^{2}}} \frac{d}{d x} (e^{x^{2}})

= e^{e^{x^{2}}} \frac{d}{d x} (e^{x^{2}})

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

= e^{e^{x^{2}}} e^{x^{2}} \cdot 2 x

Apply exponent rule:

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

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of e^{(e^{x^2}}) ?
The derivative of e^{(e^{x^2}}) is 2e^{e^{x^2}+x^2}x
What is the first derivative of e^{(e^{x^2}}) ?
The first derivative of e^{(e^{x^2}}) is 2e^{e^{x^2}+x^2}x