In mathematics, the **formal derivative** is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. The primary use of formal differentiation in algebra is to test for multiple roots of a polynomial.

Read more about Formal Derivative: Definition, Properties, Application To Finding Repeated Factors, Correspondence To Analytic Derivative

### Other articles related to "formal derivative, derivative, formal":

**Formal Derivative**- Correspondence To Analytic Derivative

... commutative, there is an alternative and equivalent definition of the

**formal derivative**, which resembles the one seen in differential calculus ... (in R) by g then it is not hard to verify that g(X,X) (in R) coincides with the

**formal derivative**of f as it was defined above ... This formulation of the

**derivative**works equally well for a

**formal**power series, assuming only that the ring of scalars is commutative ...

... Given a

**formal**power series in R], we define its

**formal derivative**, denoted Df or, by The symbol D is called the

**formal**differentiation operator ... Additionally, the

**formal derivative**has many of the properties of the usual

**derivative**of calculus ... Thus, in these respects

**formal**power series behave like Taylor series ...

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