For a univariate function, the derivative of a point is the tangent slope of a point on a plane graph; For a binary function, the derivative of a point is the tangent slope of a point on the space map.
In addition, derivatives can also be used to find the analytical expressions of monotonicity, extremum and tangent. It should be noted that not all functions have derivatives, and a function does not necessarily have derivatives at all points. If the derivative of a function exists at a certain point, it is said to be derivative at this point, otherwise it is called non-derivative. However, differentiable functions must be continuous and discontinuous functions must be non-differentiable.