I have a simple question about differentials. I have been taught two ways to find the differential and my questions is in what situations do I use each one?(adsbygoogle = window.adsbygoogle || []).push({});

simply speaking these are the 2 ways

1.) just take the partials of each component function and throw them in a matrix

2.) Let f be the function we want the differential for, where f:S→ℝ^{m}. You choose a curve [itex]\alpha[/itex](-ε,ε)→S such that [itex]\alpha[/itex](0)=p and [itex]\alpha[/itex]'(0)= v where p is in S and S is a surface, and v is in TpS.

Then you compose f with [itex]\alpha[/itex] and take the derivative with respect to t.

Thank you for your time.

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# Homework Help: Difference between 2 types of differentials?

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