Key Equations

• Partial derivative of [latex]f[/latex] with respect to [latex]x[/latex]
  [latex]\frac{\partial f}{\partial x}=\underset{h \to{0}}{\lim} \frac{f(x+h,y)-f(x,y)}{h}[/latex]
• Partial derivative of [latex]f[/latex] with respect to [latex]y[/latex]
  [latex]\frac{\partial f}{\partial y}=\underset{k \to{0}}{\lim} \frac{f(x,y+k)-f(x,y)}{k}[/latex]

Glossary

higher-order partial derivatives

second-order or higher partial derivatives, regardless of whether they are mixed partial derivatives

mixed partial derivatives

second-order or higher partial derivatives, in which at least two of the differentiations are with respect to different variables

partial derivative

a derivative of a function of more than one independent variable in which all the variables but one are held constant

partial differential equation

an equation that involves an unknown function of more than one independent variable and one or more of its partial derivatives