# Directional derivative

- Author:
- Šárka Voráčová

- Topic:
- Derivative

Partial derivative with respect to

*x*gives the rate of change of f in the*x*direction and the partial derivative with respect to y gives the rate of change of f in the*y*direction. The rate of change of a function of several variables in the direction*u*is called the*directional derivative*in the direction*u*. The directional derivative is the dot product of the gradient and the unit vector*u*, |u|=1.*z' _{u}(A) = ∇z(A) . u*

*u*is a unit vector in the*x*direction*u*= (1,0), then the directional derivative is simply the partial derivative with respect to*x*. For a general direction, the directional derivative is a combination of the partial derivatives. Problem: Cut the surface by vertical plane passing through the point*A*with the direction given by direction. Determine the slope of the intersection curve.