In the link: http://www2.imperial.ac.uk/~svanstri/Files/multivariable-calculus.pdf on the very last slide, I am confused on on why they are doing the jacobian matrix $\begin{pmatrix}\frac{du}{dx} \\ \frac{dv}{dx}\end{pmatrix}$. Can someone explain this part?
2026-04-17 12:23:42.1776428622
Implicit Function Theorem [Finding $\frac{du}{dx}$]
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It's because they were solving a system of equations with $\frac{du}{dx}$ and $\frac{dv}{dx}$ as the unknowns. A way of solving a system of linear equations is by elementary row operations.