Mechanics question derivations terminal velocity (quadratic case)

hi so basically my question is derivation of derivation of the quadratic case of the terminal velocity

I have attached the pictures in picture 1 I don’t know I think the book has error in his derivation @ equation 2.4.13 shouldn’t it be + instead of negative ??

& in second picture their is something I don’t understand two stuff acctually first is in equation 2.4.15
how did he come up with 1/2 * dv^2 / dy? and my second question is
du/dy = -1/vt^2 * dv^2/dy how did he come up with dv^2/dy ??

thanks alot.

Attached Images
File Type: jpg photo.jpg (100.6 KB)
File Type: jpg photo (1).jpg (91.9 KB)

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