Why does acceleration = $v\frac{dv}{dx}$

Question

If we define $x$ = displacement, $v$ = velocity and $a$ = acceleration then I am used to the ideas that $a= \frac{dv}{dt} = \frac{d^2x}{dt^2}$

However I also understand $a=v \frac{dv}{dx}$. Can someone explain to me why this is?

Answer 1

Notice: $\frac{dv}{dt}=\frac{dx}{dt}\frac{dv}{dx}$ by Chain rule.