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

The derivative of e^{x^x} is e^{x^x}x^x(ln(x)+1)

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

The first derivative of e^{x^x} is e^{x^x}x^x(ln(x)+1)

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derivative of

e^{x^{x}}

e^{x^{x}} x^{x} (ln (x) + 1)

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x^{x}) = x^{x} (ln (x) + 1)

= e^{x^{x}} x^{x} (ln (x) + 1)

What is the derivative of e^{x^x} ?
The derivative of e^{x^x} is e^{x^x}x^x(ln(x)+1)
What is the first derivative of e^{x^x} ?
The first derivative of e^{x^x} is e^{x^x}x^x(ln(x)+1)