Unclear equation with partial and total derivatives

Question

Suppose $M$ is a manifold and $f:M\to \mathbb{R}$ a smooth function. Also let $\alpha :I\to \mathbb{R}^n$be a representation of a curve and $(\phi,U)$ be a chart. Now why it holds that $$\frac{\partial f}{\partial x^\alpha}=\frac{d(f\circ \gamma)}{dt}$$ ?

Here, $\gamma(t)=\phi^{-1}\circ\alpha(t).$