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(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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