x^2 + z sin(xyz) = 0
2x + sin(xyz) z' + z cos(xyz) (yz + xzy' + xyz') = 0
(sin(xyz) + xyz cos(xyz))z' = -2x - z cos(xyz)(yz + xzy')
z' = -(2x + z cos(xyz)(yz + xzy') / (sin(xyz) + xyz cos(xyz)
Of course, if you just want ∂z/∂x then it's just
∂z/∂x = -(2x + yz^2 cos(xyz)) / (sin(xyz) + xyz cos(xyz)
use implicit differentiation to find dz/dx
given: x^2+zsin(xyz)=0
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