In this lesson, you will learn about the gradient vector, directional derivative, and tangent planes. The gradient vector is a vector formed by putting together all of the partial derivatives that gives you a vector field. The directional derivative is the dot product between the gradient and the velocity vector, which is also perpendicular to the level surface. The tangent plane is the best way to approximate the function at a given point, and it has the same normal vector as the surface. With this understanding, you can find the tangent plane to any surface given an equation and a point on the surface.
Learn about the gradient vector, directional derivative, and more on the tangent plane.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 15, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.