What is the derivative of e^{e^x} ?

The derivative of e^{e^x} is e^{e^x+x}

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

The first derivative of e^{e^x} is e^{e^x+x}

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derivative of

e^{e^{x}}

e^{e^{x} + x}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}

\int_{0}^{\frac{π}{4}} sec^{4} (x) d x

ln 3 x^{3} \cdot sec^{3} ({5 x + 4})

\int \frac{x + 3}{x ^{2} + 2 x} d x

\frac{\partial}{\partial x} (2 x^{3} y)

y^{^{'}} = - 2 y

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