# Parametric in $$t$$

Calculus Level 3

Given that $$x = \dfrac {t^2}2 a(t)$$ and $$y = t \cdot v(t)$$, where $$a(t)$$ and $$v(t)$$ are functions of $$t$$. Find the value of $$\dfrac{dy}{dx}$$ at $$t = 1$$ if when $$t = 1$$, $$y = 2$$, $$a(1) = 2v(1) , a'(1) = v'(1) = x$$.

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