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

The derivative of e^{x^e} is e^{x^e+1}x^{e-1}

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

The first derivative of e^{x^e} is e^{x^e+1}x^{e-1}

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derivative of

e^{x^{e}}

e^{x^{e} + 1} x^{e - 1}

Solution steps

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

Apply the chain rule:

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

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

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

= e^{x^{e}} e x^{e - 1}

Apply exponent rule:

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

e^{x^{e}} e = e^{x^{e} + 1}

= e^{x^{e} + 1} x^{e - 1}

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