Where did this y/x come from?

[ContraHacker]

Hi, this is my first post on this forum. Please help with this question.

Find d/dx of:

dy/dx = y(1 + log x)

Sol:
d2y/dx2 = y(1/x) + (1 + log x) dy/dx [Using product rule]

The next step in my textbook is

d2y/dx2 = (1/y)(dy/dx)^2 + (y/x)

This is the step which I don't understand. Thanks.

 

[Harry_the_cat]

If dy/dx = y(1+ log x) then 1 + log x = (1/y)(dy/dx)

So make that substitution after using the product rule as you have.

 

[ContraHacker]

If dy/dx = y(1+ log x) then 1 + log x = (1/y)(dy/dx)

So make that substitution after using the product rule as you have.

Ah yes! So crystal clear now. I had the feeling I was missing something really easy. Thanks a lot!