# Thread: Differentiating x to a function of x

1. ## Differentiating x to a function of x

Hi, I'm not sure how to find the derivatives of the following:
$y = x^x, y = x^{\cos x}$

I think you use a variant of the chain rule but not sure how.

Thanks

2. Take the $\ln$ of both sides,

$\ln y = \ln x^x = x \ln x$

then implicit differentiation.

3. Ahh simple stuff, thanks!