Difference between revisions of "Math 22 Partial Derivatives"
Jump to navigation
Jump to search
| Line 2: | Line 2: | ||
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_{\delta x\to 0}\frac{f(x+\delta x,y)-f(x,y)}{\delta x}</math> | |
| + | |||
| + | <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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x}
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y}
are the functions Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\partial z}{\partial x}}
and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\partial z}{\partial x}}
, defined as shown.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\partial z}{\partial x}=\lim_{\delta x\to 0}\frac{f(x+\delta x,y)-f(x,y)}{\delta x}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{\partial z}{\partial y}=\lim_{\delta y\to 0}\frac{f(x,y+\delta y)-f(x,y)}{\delta y}}
This page were made by Tri Phan