How would you solve this in a blink?

[Lorena_Santoro]

https://youtu.be/1fdk5sWG9gI

[Guest]

The problem is to differentiate [tex]y= x^x[/tex].

Take the logarithm of both sides: [tex]ln(y)= ln(x^x)= xln(x)[/tex]. Now differentiate both sides with respect to x, using the chain rule on the left and the product rule on the right.
[tex]\frac{1}{y}\frac{dy}{dx}= ln(x)- x\frac{1}{x}= ln(x)- 1[/tex].

[tex]\frac{dy}{dx}= y(x)(ln(x)- 1)= x^x(ln(x)- 1)= x^xln(x)- x^x[/tex].