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To find the total differential of $z = x^2y^2$, compute the partial derivatives with respect to x and y, then substitute them into the total differential formula. The result is $dz = 2$xy^$2 dx + 2x^2y dy$.

Conditions: The function is $z = x^2y^2$.; Standard rules of partial differentiation apply.

To find the total differential of $z = x^2y^2$, compute the partial derivatives with respect to x and y, then substitute them into the total differential formula. The result is $dz = 2$xy^$2 dx + 2x^2y dy$.

Conditions: The function is $z = x^2y^2$.; Standard rules of partial differentiation apply.