Differential Equation, Change of variables

Homework Statement

Hi,

I am looking at this question:

With this (part of ) solution:

The Attempt at a Solution

I follow up to the last line-

I do not understand here how we have simply taken the ##1/t^{\alpha m + \alpha}## outside of the derivative ##\frac{\partial}{\partial y} ## since ##y=y(r,t^{\beta}) ## i.e. ##t## and ##y## are not independent variables.... ##\frac{\partial}{\partial t}= \frac{\partial y}{\partial t^{\beta}}\frac{\partial t^{\beta}}{\partial t}##