\[\begin{align*} \boxed{\dfrac{d}{dx} \left(\dfrac{x}{3}\right) = \dfrac13} \end{align*}\]
Solving for the Derivative
We may pull the constant, $\dfrac13$, out of the derivative and focus on $\dfrac{d}{dx} x$. We may apply the power rule:
\[\begin{align*} \dfrac{d}{dx} x^n = nx^{n-1} \end{align*}\]
Doing this with $x$, which is the same as $x^1$, we get our derivative is equal to
\[\begin{align*} \dfrac{d}{dx} \left(\dfrac{x}{3}\right) &= \dfrac{1}{3} \dfrac{d}{dx} x\\ &=\dfrac13 \dfrac{d}{dx} x^1\\ &=\dfrac13 \cdot 1 \cdot x^0\\ &= \dfrac13 \cdot 1 \cdot 1\\ &=\boxed{\dfrac13} \end{align*}\]
When working with simple derivatives, it helps to factor out the constants as it breaks the derivative into elementary common derivatives. In this case, it is common knowledge that $\dfrac{d}{dx} x = 1$, so we could skip the formalities of using the power rule if we knew that from the start! The answer for any derivative of the form $\dfrac{d}{dx} kx$, where $k$ is a a real number, is just $k$.
