Essential Concepts
- A partial derivative is a derivative involving a function of more than one independent variable.
- To calculate a partial derivative with respect to a given variable, treat all the other variables as constants and use the usual differentiation rules.
- Higher-order partial derivatives can be calculated in the same way as higher-order derivatives.
Key Equations
- Partial derivative of f with respect to x
∂f∂x=limh→0f(x+h,y)−f(x,y)h - Partial derivative of f with respect to y
∂f∂y=limk→0f(x,y+k)−f(x,y)k
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
Candela Citations
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- Calculus Volume 3. Authored by: Gilbert Strang, Edwin (Jed) Herman. Provided by: OpenStax. Located at: https://openstax.org/books/calculus-volume-3/pages/1-introduction. License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike. License Terms: Access for free at https://openstax.org/books/calculus-volume-3/pages/1-introduction