Math 2.0

statement corollary

Constant multiple rule

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.

Explanations

L1 human

Stretching a graph vertically by a factor cc multiplies all its slopes by cc.

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To read this node, read these 10 nodes in this order. The foundations come first, and the list ends with this node.

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 node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
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  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

Sources

  1. Web https://en.wikipedia.org/wiki/Linearity_of_differentiation, Constant coefficient

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