Let $U \subset \mathbb{R}^n$ be open, let $a \in U$, let $f: U \to \mathbb{R}$ be differentiable at $a$, and let $\varepsilon > 0$. Suppose $\gamma: (-\varepsilon,\varepsilon) \to U$ is differentiable at $0$, satisfies $\gamma(0)=a$, and has derivative $\gamma'(0)=v \in \mathbb{R}^n$. Then $f \circ \gamma: (-\varepsilon,\varepsilon) \to \mathbb{R}$ is differentiable at $0$, and

\begin{align*} (f \circ \gamma)'(0) = D_v f(a), \end{align*}

where $D_v f(a) = Df_a(v)$ is the [directional derivative](/page/Directional%20Derivative) of $f$ at $a$ in the direction $v$.