Derivative of FunctionsSuppose that there is y=f(x) on the interval [a;b]. We increment D х totheargument х; then the function obtains the following increment у®у+ D у, у+ D у=f (х+ D х),D у=f (х+ D х) –у.
f(x+Dx) f(x) 0 x x+Dx х
Definition. The ratio limit of a function increment to an argument increment, where the latter tends to zero, is called a derivative of function. Notation:
The notations in the form of f¢(x), у¢ or у¢х are the Lagrange notations, and the notations of the form
|
у
. (1)
or 
are the Leibniz notations.
