Derivative of a Constant Function
d/dx(x) = 1
The derivative of a constant function is always 0.
This is because the derivative of a function represents the rate of change of the function at any given point. A constant function has a constant value and therefore does not change at any point, meaning its rate of change is always 0.
Symbolically, if f(x) = c (where c is a constant), then
f'(x) = lim(h->0) (f(x+h) – f(x)) / h
= lim(h->0) (c – c) / h
= lim(h->0) 0 / h
= 0
Therefore, the derivative of a constant function is always 0.
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