Differentiating y=x^x(adsbygoogle = window.adsbygoogle || []).push({});

x=ln(y)

I changed the base to e

[tex]x=\frac{ln(y)}{ln(x)}[/tex]

[tex]xln(x) = ln(y)[/tex]

[tex]e^{xln(x)} = y[/tex]

[tex]e^{xln(x)}(1+ln(x) = \frac{dy}{dx}[/tex]

The answer the calculator got was [tex]x^{x(1+ln(x))}[/tex] so I noticed that since [tex]y=x^x[/tex] and [tex]e^{xln(x)} = y[/tex], then I could replace it with x^x in the final answer

Is this an acceptable method? Is there any circular logic I missed? Could I leave it as is wihtout writing x^x?

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# Differentiating y=x^x

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