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I am searching for a book on multi-variable calculus that explains multi-variable product, multi-variable integration by parts, etc.

As an example, here's a simple problem that I would like to be able to do after reading this book.

Let u(x) = || x - y ||^2 + 3x^t z. Find the derivative of u with respect to x.

Can anyone recommend a book to me?

Thank you for your help.

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The free book Vector Calculus by Corral covers enough of differentiation for your immediate needs. Multivariable integral identities are covered more thoroughly in Vector Calculus by Marsden and Tromba. Or you can dive right into Zorich.

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Introduction to Electrodynamics by Griffiths has exactly the material that I was looking for, and it is explained well.

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