Difference between revisions of "Math 22 Partial Derivatives"
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If <math>z=f(x,y)</math>, then the first partial derivatives of with respect to <math>x</math> and <math>y</math> are the functions <math>\frac{\partial z}{\partial x}</math> and <math>\frac{\partial z}{\partial x}</math>, defined as shown. | If <math>z=f(x,y)</math>, then the first partial derivatives of with respect to <math>x</math> and <math>y</math> are the functions <math>\frac{\partial z}{\partial x}</math> and <math>\frac{\partial z}{\partial x}</math>, defined as shown. | ||
| − | <math>\frac{\partial z}{\partial x}=\lim_{\ | + | <math>\frac{\partial z}{\partial x}=\lim_{\Delta x\to 0}\frac{f(x+\Delta x,y)-f(x,y)}{\Delta x}</math> |
| − | <math>\frac{\partial z}{\partial y}=\lim_{\ | + | <math>\frac{\partial z}{\partial y}=\lim_{\Delta y\to 0}\frac{f(x,y+\Delta y)-f(x,y)}{\Delta y}</math> |
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 07:27, 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.
This page were made by Tri Phan