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Proof: Constant Rule
(Math | Calculus | Derivatives | Identities | Constant Rule)
(d/dx) c f(x) = c (d/dx) f(x)


Proof of (d/dx) c f(x) = c (d/dx) f(x) from the definition

We can use the definition of the derivative:

(d/dx) f(x) = lim
d-->0  
f(x+d)-f(x)
d
Therefore, (d/dx) c f(x) can be written as such:
(d/dx) c f(x) =
lim
d-->0  
cf(x+d) - cf(x)
d
c lim
   d-->0  
f(x+d) - f(x)
d
= c * (d/dx) f(x)


  
 
  

 
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