What are Directional Derivatives and How Can They Be Calculated?

[The_Teacher]

Hey there, as part of my first year in engineering I'm doing some challenging math that i can usually make sense of by myself apart from these Directional Derivatives. If someone could explain these to me in both straightforward terms first and more complicated math theory second it would be greatly appreciated! thanks!

 

[Defennder]

Try Wikipedia or your maths textbook.

 

[HallsofIvy]

If z= F(x,y), then z has a value at every point in the plane. A "directional derivative" just tells the derivative (rate of change) of z in a particular direction. There are several different ways to find that. One would be to change to a new coordinate system so the the x' axis pointed in the given direction and the y' axis perpendicular to it. Then the directional derivative is just the partial derivative with respect to x'. Another is to calculate the gradient. The directional derivative is the wdot product of the gradient vector and the unit vector in the given direction.