Partial derivative with respect to [i]x[/i] gives the rate of change of f in the [i]x[/i] direction and the partial derivative with respect to y gives the rate of change of f in the [i]y[/i] direction. [br][br]The rate of change of a function of several variables in the direction [i]u[/i] is called the [i]directional derivative[/i] in the direction [i]u[/i]. The directional derivative is the [url=https://math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/dotprod/dotprod.html]dot product[/url] of the gradient and the [url=https://en.wikipedia.org/wiki/Unit_vector]unit[/url] vector [i]u[/i], |u|=1.[br][center][i]z'[sub]u[/sub](A) = ∇z(A) . u[/i][/center]Note that if [i]u[/i] is a unit vector in the [i]x[/i] direction [i]u [/i]= (1,0), then the directional derivative is simply the partial derivative with respect to [i]x[/i]. For a general direction, the directional derivative is a combination[br]of the partial derivatives.[br][br]Problem: Cut the surface [math]z=4-\sqrt{x^2+y^2}[/math] by vertical plane passing through the point [i]A[/i] with the direction given by direction. Determine the slope of the intersection curve.