Question

Derivative of a constant is 0!? o.O How come?

Answer 1

A constant function is just a horizontal line. Slope of a horizontal line is 0.

Answer 2

And since the slope of a function at a point is a derivative at that point, derivative of any constant is 0

Answer 3

Oh I see, thanks :)

Answer 4

Derivative represents the small change in something..
As constant is a value that remains same, so there is 0 change in the constant...

Answer 5

Agent47 earned a fan.

Answer 6

Got it, thanks guys! :)

Answer 7

if you want to be silly you can prove it directly from the difference quotient
let \(f(x)=c\) then
\[\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{x\to 0}\frac{c-c}{0}=0\]

Answer 8

@zepp , your fav method^

Answer 9

typo
\[\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}=\lim_{h\to 0}\frac{c-c}{h}=0\]

Answer 10

You know me so well, saif ;D

Thanks @satellite73!