d/dx[c]
0
The derivative of a constant value, such as c, with respect to any variable, including x, is always zero.
This can be demonstrated using the definition of a derivative:
lim h->0 [f(x+h) – f(x)]/h
If f(x) = c, then f(x+h) = c, since c is a constant that does not change with the addition of h. Substituting these values into the definition of the derivative, we get:
lim h->0 [c – c]/h
Simplifying this expression:
lim h->0 0/h
Which evaluates to zero.
Therefore, the derivative of a constant value c with respect to any variable x is zero:
d/dx[c] = 0.
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