DIFFERENTIATION

I wonder is there a way to calculate something like this:

y=x^((x^(x^4))+(x^4)-1)

Is it possible to calculate dy/dx?
I tried to use logarithmic differentiation and I was stuck in the middle of it.

ln y = ((x^(x^4))+(x^4)-1) ln x
Then how can I differentiate ((x^(x^4))+(x^4)-1)??

Thx.