Math 2.0

Real functions Corollary

Constant multiple rule

Builds on Linearity of differentiation

Statement

Let ff be a real function on an open interval II, differentiable at a∈Ia \in I, and let cc be a real number. Then cfc f is differentiable at aa, and (cf)′(a)=cf′(a)(c f)'(a) = c f'(a).

Remarks

It is the case β=0\beta = 0 of the linearity of differentiation. For example, (5x2)′=10x(5 x^2)' = 10 x. Mathlib states it as deriv_const_mul.

Reading path

To understand this page from the ground up, read these 10 pages in order. The foundations come first.

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Limit point of a set, definition, no evidence levelLimit point of a setdefinitionSequence, definition, no evidence levelSequencedefinitionLimit of a function, definition, no evidence levelLimit of a functiondefinitionReal sequence, definition, no evidence levelReal sequencedefinitionDerivative, definition, no evidence levelDerivativedefinitionLimit of a sequence, definition, no evidence levelLimit of a sequencedefinitionEpsilon-N definition of the limit of a sequence, statement, no evidence levelEpsilon-N definition …statementLimit of a sum of sequences, statement, no evidence levelLimit of a sum of seq…statementLinearity of differentiation, statement, no evidence levelLinearity of differen…statementConstant multiple rule, statement, no evidence levelConstant multiple rulestatement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Limit point of a set definition
  2. Sequence definition
  3. Limit of a function definition
  4. Real sequence definition
  5. Derivative definition
  6. Limit of a sequence definition
  7. Epsilon-N definition of the limit of a sequence statement
  8. Limit of a sum of sequences statement
  9. Linearity of differentiation statement
  10. Constant multiple rule statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Linearity_of_differentiation, Constant coefficient
About this page
Tag0Z9JB71BS0
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Kindstatement, corollary
WritingW0 stub
MSC26A24
StatusThis copy of the site has no build data. Run m2 status 0Z9JB71BS0.
UsesLinearity of differentiation

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