Think of a gradient as a kind of vector slope. In one dimension, the derivative of a function is its slope at any given point; since in this case there is only

Think of a gradient as a kind of vector slope. In one dimension, the derivative of a function is its slope at any given point; since in this case there is only one direction against which to measure the slope, we would typically consider the derivative of a single variable function to be a scalar rather than a vector. For a multivariable function, the gradient points in the direction of maximum ascent, and its magnitude is the steepness with which the (graph of the) function (which is a surface) changes in that direction.