When the dot product is taken between this and any unit vector, the directional derivative is obtained.
When the dot product is taken between this and any unit vector, the directional derivative is obtained. Line integrals through it are path independent, as shown by its namesake theorem, which is also known as the fundamental theorem of calculus for line integrals. The tangent plane to any level surface is defined with this as the normal vector. The maximum value of the directional derivative at a point is its magnitude and is in the same direction as its vector. For 10 points, name this vector field denoted by nabla f and defined as the vector field whose components are the partial derivatives of f.
When the dot product is taken between this and any unit vector, the directional derivative is obtained.
{Gradient}