Math 22 Partial Derivatives

Partial Derivatives of a Function of Two Variables

 If $z=f(x,y)$, then the first partial derivatives of  with respect to $x$ and $y$ are the functions ${\frac {\partial z}{\partial x}}$ and ${\frac {\partial z}{\partial x}}$, 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}}

 
 ${\frac {\partial z}{\partial y}}=\lim _{\Delta y\to 0}{\frac {f(x,y+\Delta y)-f(x,y)}{\Delta y}}$

Example: Find ${\frac {\partial z}{\partial x}}$ and ${\frac {\partial z}{\partial y}}$ of

Return to Topics Page

This page were made by Tri Phan