derivative of x^{2x}

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ddx (x^2x)=2x^2x(ln(x)+1)

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ddx (x^2x)=2x^2x(ln(x)+1)

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ddx (x^2x)

Apply exponent rule: a^b=e^bln(a)
x^2x=e^2xln(x)
=ddx (e^2xln(x))

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Apply the chain rule: e^2xln(x)ddx (2xln(x))
=e^2xln(x)ddx (2xln(x))

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ddx (2xln(x))=2(ln(x)+1)
=e^2xln(x)· 2(ln(x)+1)

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e^2xln(x)=x^2x
=2x^2x(ln(x)+1)