I have a scalar function f dependent on a few variables $x_i$, and I would like to change variables, so that [tex]y_i = \sum_j {M_{ij} x_j},[/tex] where M is an invertible matrix independent of the x_i-s, and compute:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\frac{\partial f}{\partial x_i} = \frac{\partial f}{\partial \left( \sum_j {M^{-1}_{ij} y_j} \right)} = \sum_j Q_{ij} \frac{\partial f}{\partial y_j}

[/tex]

I suggest that the last identity is true for some matrix Q. Is there a general formula for Q?

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# Multivariable calculus question

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