The derivative of $\dfrac{x}{5}$ is $\boxed{\dfrac{1}{5}}$.

To find the derivative of $\dfrac{x}{5}$, we may apply the power rule:

\[\begin{align*} \dfrac{d}{dx} x^n = nx^{n – 1} \end{align*}\]

In this case, $\dfrac{x}{5}$ can be rewritten as $\dfrac{1}{5} \cdot x^1$, where the coefficient $\dfrac15$ is constant and \(x\) has an exponent of \(n=1\).

### Solution

Using the power rule:

\[\begin{align*} \dfrac{d}{dx} \dfrac{x}{5} &= \dfrac{1}{5} \cdot \dfrac{d}{dx} (x^1) \\ &= \dfrac{1}{5} \cdot (1)(x^{1 – 1}) \\ &= \dfrac{1}{5} \cdot 1 \cdot x^0 \\ &= \dfrac{1}{5} \cdot 1 \cdot 1 \\ &= \boxed{\dfrac{1}{5}} \end{align*}\]

### Explanation

The derivative of \(\dfrac{x}{5}\) is \(\dfrac{1}{5}\), which makes sense because the slope of any linear function of the form \(mx\) is simply the coefficient \(m\). Here, the coefficient is \(\dfrac{1}{5}\), so the slope and derivative of the function are both \(\dfrac{1}{5}\).

This result tells us that the rate of change of the function \(\dfrac{x}{5}\) is constant. No matter the value of \(x\), the slope remains the same, which is a characteristic of linear functions.