Question

Differentiate `y=x^x`?

Answer 1

`(dy)/(dx)=(1+lnx)x^x`

Explanation:

As `y=x^x`, we have `lny=lnx^x=xlnx`

Hence differentiating both sides, `1/yxx(dy)/(dx)=1xxlnx+x xx1/x`

or `1/(x^x)xx(dy)/(dx)=1+lnx` and hence

`(dy)/(dx)=(1+lnx)x^x`