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Exploring Higher-Order Partial Derivatives with Mixed Partial Derivatives

Learn about second, third, and higher-order partial derivatives and their significance in finding maximums and minimums. Understand the concept of mixed partial derivatives and their equality. Explore examples of partial derivatives of functions with three or more variables.

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Exploring Higher-Order Partial Derivatives with Mixed Partial Derivatives

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  1. 13.3 day 2 Higher- Order Partial Derivatives

  2. Higher- Order Partial Derivatives As is true for ordinary derivatives, it is possible to take second, third and higher order derivatives provided such derivatives exist.

  3. Higher-Order derivatives:

  4. Higher-Order partial derivatives Note: we will need to use all 4 of these second order partial derivatives in a later section to find maximums and minimums.

  5. Mixed Partial derivatives: Both answers are the same!

  6. Equality of Mixed Partial Derivatives

  7. Example 8

  8. Example 8 Solution

  9. Partial derivatives of a function of 3 or more variables

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