## derivative of a constant, f(x)=45

### The derivative of a constant is always zero

The derivative of a constant is always zero. In this case, since the function f(x) is defined as f(x) = 45, the derivative of f(x) with respect to x would be zero. Mathematically, it can be written as:

f'(x) = 0

This is because the derivative of a constant function is independent of x and only measures the rate of change of the function. Since a constant does not change, its rate of change is zero.

In other words, no matter what value of x you choose, the derivative of a constant function will always be zero. This concept is important in calculus as it helps us to study how functions change and relate to each other.

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