u = x ^ 2 - 2y v = x + y + z ; w = x - 2y + 3z find partial (u, v, w) partial(x,y,x)

To find the partial derivatives of the functions \( u \), \( v \), and \( w \) with respect to the variables \( x \), \( y \), and \( z \), we need to compute the Jacobian matrix. The Jacobian matrix \( J \) of the transformation from \((x, y, z)\) to \((u, v, w)\) is given by:

\[ J = \begin{pmatrix}
\frac{\partial u}{\partial x} & \frac{\partial u}{\partial y} & \frac{\partial u}{\partial z} \\
\frac{\partial v}{\partial x} & \frac{\partial v}{\partial y} & \frac{\partial v}{\partial z} \

Learn how to compute partial derivatives of multivariable functions u, v, and w with respect to variables x, y, and z. This problem involves calculating the Jacobian matrix, which is crucial in vector calculus and differential geometry. Suitable for advanced undergraduate students and researchers.

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