# Difference between revisions of "Math 22 Partial Derivatives"

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− | ''' | + | '''2)''' <math>z=f(x,y)=x^2y^3</math> |

{| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | {| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | ||

!Solution: | !Solution: | ||

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− | + | '''3)''' <math>z=f(x,y)=x^2e^{x^2y}</math> | |

+ | {| class = "mw-collapsible mw-collapsed" style = "text-align:left;" | ||

+ | !Solution: | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial x}=2xe^{x^2y}+x^2e^{x^2y}2xy</math> (product rule +chain rule) | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial y}=x^2e^{x^2y}x^2</math> | ||

+ | |} | ||

## Revision as of 08:37, 18 August 2020

## 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) |

**This page were made by Tri Phan**