What is a partial derivative?
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Partial derivatives are used to take derivatives of functions that have multiple variables.
Scenario: Evaluate the derivative of the function below with respect to y.
The fact that we're evaluating the derivative with respect to y means that we'll treat x as a constant!
With partial derivatives, treat the extra variable(s) that you're not evaluating the derivative with respect to as a constant.
Scenario: Evaluate the derivative of the function below with respect to x and then y.
In this situation, we'd make two runs:
- Evaluate the derivative with respect to x (and treat y as a constant)
- And then [do the exact same thing with] y (and treat x as a constant)