Recently I started with multivariable calculus; where I have seen concepts like multivariable function, partial derivative, and so on. A week ago we saw the following concept: directional derivative. Ok, I know the math behind this as well as the way to compute the directional derivative through the dot product of the gradient and the unit vector: Duf(x,y)=∇f(x,y)⋅uWhere: Duf(x,y) represents the directional derivative ∇f(x,y) represents the gradient u represents the unit vector Ok, I know the equation, but my questions are the following: what's exactly a directional derivative? what's a gradient? for what are they used? Thanks.