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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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