The Chain Rule

الملخص

     When it comes to the calculation of derivatives, there is a rule for derivatives: either the function is basic, in which case we can appeal to the table of derivatives, or the function is composite, in which case we can differentiated it recursively by breaking it down into the derivatives of it`s constituents via series of derivative rules, and in single – variable calculus, we fund that one of the most useful differentiation rules is (The Chain Rule), which allows us to find the derivative of composition of two (or more than) functions. The same thing is true for multivariable calculus, but is time we have to deal with more than one form of The Chain Rule. This research is about The Chain Rule in calculus, and we study the extension of the chain rule and learn how to take the derivatives of composition of more than two functions and of more than one variable, and with some applications on it.