Partial Derivatives of Functions of More than one independent variable

1.

In a Nut Shell: The derivative of a function of one independent variable (say x) relates directly to the slope of the dependent variable (say y). i.e. dy/dx Likewise for function z of two independent variables (say x and y), the partial derivative on x gives the slope in the x-direction and the partial derivative on y gives the slope in the y direction. i.e. ∂z/∂x and ∂z/∂y The notion of partial derivatives holds for functions of any number of independent variables.

2.

Let’s start by reviewing the situation of a function of only one independent variable, x. Recall the definition of the derivative for a function of one independent variable, x f ’(x) = lim [ f(x + h) - f(x)]/ h h → 0 With one independent variable, f ’(x) represents the slope of the curve f(x) at point P. Click here to continue with discussion of partial derivatives.

Return to Calculus 3 Notes

Copyright © 2013 Richard C. Coddington

All rights reserved