Basic Derivative Rules

Thomas J. Pfaff ()
Additional contact information
Thomas J. Pfaff: Ithaca College, Department of Mathematics

Chapter Chapter 11 in Applied Calculus with R, 2023, pp 145-155 from Springer

Abstract: Abstract The definition of the derivative function given in M-Box 10.2 is time-consuming to apply to every function for which we want a derivative. For example, the derivative of $$f(x)=3x^2$$ f ( x ) = 3 x 2 , $$f(x)=5x^2$$ f ( x ) = 5 x 2 , and $$f(x)=7x^2$$ f ( x ) = 7 x 2 would each be a similar yet separate calculation. It turns out we can use the definition of the derivative in M-Box 10.2 to derive general rules so that we do not need to use the limit formula each time. M-Box 11.1 lists basic rules of derivatives. Note that all of these rules are derived by definition of the derivative in M-Box 10.2 . They are not definitions but the result of applying a definition. We prove rule 11.2 and note that the case $$n=2$$ n = 2 for rule 11.3 was done in example 10.2 .

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-28571-4_11

Ordering information: This item can be ordered from
http://www.springer.com/9783031285714

DOI: 10.1007/978-3-031-28571-4_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().