# Unclear equation with partial and total derivatives

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

• Whats the expression in the LHS ? I think its incomplete. – Sou Dec 5 '17 at 15:31
• @Sou燈馬想 It is the $\alpha$-th coordinate curve where $x^{\alpha}(\gamma(t))=t+const$ – user122424 Dec 5 '17 at 15:33
• I'm sorry but i cant understand what you're asking. – Sou Dec 5 '17 at 15:36
• @Sou燈馬想 Oh, sorry. Fixed now.$\partial$ was missing there. – user122424 Dec 5 '17 at 15:38
• @Sou燈馬想 Is it OK now?I've added one line below the question. – user122424 Dec 5 '17 at 16:09