Given a Function F(x,y,z), and I want to calculate the derivative of the function with respect to x,y and z, forward mode generally will take 3 passes to compute the derivative, one pass for each x,y and z. However I read that in vector mode, we can avoid the recalculation of some directional derivatives and that the derivative with respect to x,y and z can be calculated in one pass. Can some one explain how this can be done? And how does one leverage the directional derivatives? Does the overall time complexity change when we do it in one pass?