derivative of a constant:d/dx [c] = ___________________
0
The derivative of a constant c is 0.
To understand this, we need to remember that the derivative of a function is a measure of how much the function changes as its input changes. Since a constant function never changes, its derivative is always zero.
We can also use the definition of the derivative to see this. Let f(x) = c be a constant function. Then by definition, the derivative of f with respect to x is:
f'(x) = lim (h -> 0) [(f(x + h) – f(x))/h]
= lim (h -> 0) [(c – c)/h]
= lim (h -> 0) [0/h]
= 0
So the derivative of a constant function with respect to its input is always 0.
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