In the chain rule shouldn’t it be $\sigma_{\tilde u}$ for the second one? How do they get just $\sigma_u$ for both? Can someone clarify this please?
2026-03-29 17:43:54.1774806234
Help Needed! Confusion with chain Rule. Someone clarify please.
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No, it is not a typo. $\sigma(u,v)$ is the given parametrization of the surface. Its partial derivatives are $\sigma_u$ and $\sigma_v$. You are going to plug in $u=u(t)$ or $u=\tilde u(t)$ to make your composed function. Perhaps it would be better to write $\sigma(g(t),h(t))$ and $\sigma(\tilde g(t),\tilde h(t))$ so you don't get confused. The multivariable chain rule is the most maligned creature on earth.