Directional derivatives

• Are Directional Derivatives Scalars or Vectors?
  A directional derivative is scalar for a scalar-valued function and vector-valued for a vector-valued function; the direction itself is an input vector.
• How to Find the Steepest Slope of a Mountain
  For an elevation function h(x,y), the steepest local slope is the gradient’s magnitude; its direction is the gradient, with units converted consistently.
• How to Find the Steepest Slope Without Coordinates
  For a differentiable surface z=f(x,y), the steepest directional slope at a point is the gradient's magnitude, attained in the gradient direction.