Final answer:
The derivative of the function y=[cos(\(\frac{\pi}{2}\))-x] is -1. This is because cos(\(\frac{\pi}{2}\)) is 0, making the function simply -x, whose slope and therefore derivative is a constant -1.
Step-by-step explanation:
The question you've asked involves finding the derivative of the function y=[cos(\(\frac{\pi}{2}\))-x]. The derivative of a function generally represents the rate at which the function's value changes with respect to a change in its input variable. Derivatives are a fundamental tool in calculus used to find slopes of tangents, rates of change, and solve many other problems in mathematics, physics, engineering, and economics.
Step-by-step explanation
First, let's simplify your function. The term cos(\(\frac{\pi}{2}\)) is a constant since \(\frac{\pi}{2}\) is a fixed number. The cosine of \(\frac{\pi}{2}\) radians is 0, so your function effectively reduces to y = -x. Now, let's find the derivative of y with respect to x.
The derivative of -x with respect to x is simply -1 because the slope of y = -x is constant and equals -1. This can also be remembered as a basic rule that the derivative of any linear function ax + b is a, where a is the coefficient of x.
Thus, the derivative of y is -1. This means for any small change in x, y will change by the same amount in the opposite direction.