# Math 22 Partial Derivatives

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## Partial Derivatives of a Function of Two Variables

If , then the first partial derivatives of with respect to and are the functions and , defined as shown. We can denote as and as

**Example:** Find and of:

**1)**

Solution: |
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**2)**

Solution: |
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**3)**

Solution: |
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(product rule +chain rule) |

## Higher-Order Partial Derivatives

1. **Failed to parse (unknown function "\f"): {\displaystyle \frac{\partial}{\partial x}(\frac{\partial f}{\partial x})=\frac{\partial^2 f}{\partial x^2}=\f_{xx}}**
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