Question on chain rule and composition

Question

I am struggling to apply multi dimensional chain rule to a double composition. In particular how do I calculate :

$$\frac{d}{dt}\big(F\circ f_t \circ g_t \big)$$

where $F:\mathbb{R}^d\to \mathbb{R}$, and $f_t,g_t :\mathbb{R}^d\to \mathbb{R}^d$.