When a curve is given by the parametric equations $x=f(t)$ and $y=g(t),$ then $\frac{dy}{dx}$ can be found by calculating

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{g^{\text{'}}(t)}{f^{\text{'}}(t)}$

We have $x=e^{\sqrt[\phantom{2}]{t}}$ and $y=t-ln{t}^3.$ Since $x=f(t)=e^{\sqrt[\phantom{2}]{t}}$ is a componition, then by the Chain Rule we have

$x(t)-$

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