I am stuck with this problem, please explain how to do it, more importantly, why, what concept and what principle is used, thanks

f'(x^x), the answer is: (x^x)*(1+ln(x))

 

I am stuck with this problem, please explain how to do it, more importantly, why, what concept and what principle is used, thanks

f'(x^x), the answer is: (x^x)*(1+ln(x))

Here is a hint. Take any expression. Then take the natural logarithm of it. Then take the exponential of it. That expression is unchanged. In other words take a funtion y(x). The following is true.

y(x)=exp(ln(y))

So, can you find the derivative of exp(ln(x^x))?

 

your hints is a lot better than WolframAlpha, nice and easy to understand

I solved it now, thanks a lot