Question

Use logarithmic differentiation

Y=x^x^3

Answer 1

I will assume you mean:

y = x^(x^3) , then
ln y = (x^3)(ln x) according to the rules of logs
take derivative with respect to x
(dy/dx) / y = (x^3)(1/x) + 3x^2 lnx , using the product rule
dy/dx / y = x^2( 1 + 3 lnx)
dy/dx = y x^2(1 + 3lnx)