Question

what is the derivative of a constant, c?

Explanation:

Step1: Use the derivative formula

The derivative formula for a function \(y = f(x)\) is \(y^\prime=\lim\limits_{\Delta x
ightarrow0}\frac{f(x + \Delta x)-f(x)}{\Delta x}\). For \(y = c\) (where \(c\) is a constant), \(f(x)=c\) and \(f(x+\Delta x)=c\).

Step2: Calculate the derivative

Substitute into the formula: \(\frac{c - c}{\Delta x}=0\) as \(\Delta x
ightarrow0\).

Answer:

\(0\)