What is differentiate in mathematics?

Answer 1

Calculus! So, when you differentiate a function or find the derivative, as it is also called, you are finding the rate of change of the function. An easy way to find the derivative at a certain point on a function is to draw a line tangent to the function at that point; the slope of the tangent line is the derivative.

Answer 2

The word "differentiate" commands the application of the differential operator to a function, i.e. it refers to the notion of differentiation. Consider the most basic notion of a function which is merely a rule which assigns to a real number x some other real number called f(x). The derivative of the function f is the limit of the so-called difference ratio (f(x+h)-f(x))/h as h tends to 0. Notice that in order to understand what the derivative is, you must clearly understand what is meant here by the "limit" of the difference ratio. The words "differentiate", "differentiation", and "derivative" are in a certain sense used in the same way that the words "add", "addition", and "sum" are used to describe addition (although of course addition is a different type of operation entirely)