i'm having problems when needed to show stuff like this ... i don't have problems applying those rules to solve some concrete problems (calculating them) but with this i'm clueless so any help would be greatly grateful

i need to do... if for the function $\displaystyle f: \mathbb{R} ^n \to \mathbb{R} $ we put $\displaystyle g(t) = f(t,x_2, . . . , x_n)$ show that $\displaystyle g'(t) = D_{e_1} f(x_1,x_2, . . . , x_n) $