Derivatives of Parametric Curves Worksheet with Answer Key

What's on the worksheet

1. Find dydx as a function of t and simplify.
   x = \sin 2t, y = \cos^2 tx = \ln(t^2 + 1), y = \arctan tx = te^t, y = e^{2t}
2. Find the tangent line to the curve x = t² + 4t, y = t³ - 4t² at the point (5, −3).
3. A point moves along x = e^t², y = t for -1 ≤ t ≤ 1.
4. For the curve x = t³ - 3, y = -3t² - 2t, find dydx and d²ydx² at t = -2.
5. Consider the curve x = t³ - 3t, y = t².
6. Leah flies a survey drone in a loop over a field.
7. Samir skates a trick line in a flat skate park plaza, filmed by a camera on a tall pole.