Solution
= Solution
At fixed $t$, the argument is linear in $x$, with $\partial s/\partial x=b^at^a$. Each <differentiation> therefore contributes this same constant factor, while the outside factor $t^a$ remains unchanged. Thus
$$
\boxed{\frac{\partial^3u}{\partial x^3}=t^a(b^at^a)^3y^{(3)}(s)=b^{3a}t^{4a}y^{(3)}(s).}
$$
Here $y^{(3)}$ denotes the third <derivative> of the single-variable profile, not a partial <derivative> of $u$.