Where did Euler first write about homogeneous function

Question

I have seen many times that an Euler homogeneous function of degree $k$ takes the form $$f(\lambda x) = \lambda^k f(x).$$ From here one can go on about the first and second derivatives of this Euler homogeneous function. However where did Euler actually write about this stuff? For instance, some refer to $$ \nabla f(\mathbf{x})^\top \mathbf{x} = kf(\mathbf{x}) $$ as Euler's first theorem for homogeneous functions or Euler's homogeneous function theorem, but there are no references to any of his work.

Answer 1

I found his original thoughts in the translated version of "Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum, volume 1", chapter 7. The translation is called "Foundations of Differential Calculus" and a link is found here https://link.springer.com/book/10.1007%2Fb97699 .