Partial derivatives as slopes of tangent lines
Imagine a surface and consider a particular point in its domain, . As one "moves through" in the -plane, traveling in the positive -direction, the value of changes - the rate at which changes is called the partial derivative of with respect to at , and is denoted . Similarly, one finds the partial derivative of with respect to , by moving through in the positive direction.
In the interactive figure, select (or create) a surface , and use the sliders to position the point . By viewing cross-sections of the surface, you can see the partial derivatives of at that point as slopes of certain lines tangent to the surface through the point .
Developed for use with Thomas' Calculus, published by Pearson.