Partial Derivatives
Given a function of multiple variables the partial derivative is the tangent plane at a given input. Partial Derivatives are the inverse operation of multiple integrals.
revise above -- is it truly a plane or are they lines?
They use a similar notation to derivatives of one variable but use a slightly modified version, see partial derivative notation.
See Multivariable Calculus Notes - Chapter 14 - Sections 3-4 for more info about partial derivatives.
Finding Partial Derivatives
expand
When taking the partial derivative of a function you hold one of the variables as a constant and the other as a variable.
Implicit Differentiation
When trying to find implicit derivatives you can use the the chain rule for partial derivatives. See Multivariable Calculus Notes - Chapter 14 - Sections 5-6.
Related Topics
- A matrix of partial derivatives is called a Jacobian Matrix.
- When given a solid, one can use partial derivatives to find a plane tangent to the solid at a point within it's domain. One can also find a line along this plane, or a directional derivative.
Interactive Graph