# How do you differentiate the following parametric equation: # x(t)=t-cos^2t, y(t)=tsint #?

Given that

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To differentiate the parametric equations (x(t) = t - \cos^2(t)) and (y(t) = t \sin(t)), you'll need to use the chain rule and product rule where necessary. Here are the derivatives:

[ \frac{{dx}}{{dt}} = 1 + 2\cos(t)\sin(t) ]

[ \frac{{dy}}{{dt}} = \sin(t) + t\cos(t) ]

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