# Difference between revisions of "Math 22 Partial Derivatives"

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<math>\frac{\partial z}{\partial y}=\lim_{\Delta y\to 0}\frac{f(x,y+\Delta y)-f(x,y)}{\Delta y}</math> | <math>\frac{\partial z}{\partial y}=\lim_{\Delta y\to 0}\frac{f(x,y+\Delta y)-f(x,y)}{\Delta y}</math> | ||

+ | |||

+ | We can denote <math>\frac{\partial z}{\partial x}</math> as <math>f_x(x,y)</math> and <math>\frac{\partial z}{\partial y}</math> as <math>f_y(x,y)</math> | ||

+ | '''Example:''' Find <math>\frac{\partial z}{\partial x}</math> and <math>\frac{\partial z}{\partial y}</math> of: | ||

− | ''' | + | '''1)''' <math>z=f(x,y)=2x^2-4xy</math> |

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

+ | !Solution: | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial x}=4x^2-4y</math> | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial y}=-4x</math> | ||

+ | |} | ||

+ | '''1)''' <math>z=f(x,y)=x^2y^3</math> | ||

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

+ | !Solution: | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial x}=4x^2-4y</math> | ||

+ | |- | ||

+ | |<math>\frac{\partial z}{\partial y}=-4x</math> | ||

+ | |} | ||

## Revision as of 07:35, 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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**1)**

Solution: |
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**This page were made by Tri Phan**