Find dz/dy for the following :

Question

xln(1-2y) = zsin((x^2)z)-3y+z

Answer 1

x ln(1-2y) = z sin((x^2)z)-3y+z
x (-2/(1-2y)) = z' sin((x^2)z)
+ z cos((x^2)z)(x^2 z') - 3 + z'

z' =
(2x/(2y-1) + 3)
-------------------------------------
sin((x^2)z) + x^2z cos((x^2)z) + 1