Find the derivative of the given function.
[tex]
\begin{array}{l}
f(x)=2 \pi-7 \\
f^{\prime}(x)=[?]
\end{array}
[/tex]
Answer (1)
Recognize that f ( x ) = 2 π − 7 is a constant function.
Recall that the derivative of any constant is zero.
Apply the constant rule to find f ′ ( x ) = 0 .
The derivative of the function is 0 .
Explanation
Analyze the function The given function is f ( x ) = 2 π − 7 . We need to find its derivative, f ′ ( x ) .
Recognize constant term Notice that 2 π is a constant, and 7 is also a constant. Therefore, 2 π − 7 is a constant.
Derivative of a constant The derivative of a constant is always zero. This is a fundamental rule in calculus.
Find the derivative Therefore, the derivative of f ( x ) = 2 π − 7 is f ′ ( x ) = 0 .
Examples
In physics, if you have a potential energy function that is constant, like U ( x ) = 5 Joules, it means the potential energy doesn't change with position. The force, which is the negative derivative of the potential energy, would be zero, indicating no force is acting on the object. This concept is crucial in understanding equilibrium states where no net force is present.
