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Derivatives of Parametric Equations — dy/dx = (dy/dt)/(dx/dt)

If x=f(t), y=g(t), then dy/dx = (dy/dt)/(dx/dt) = g'(t)/f'(t). Use chain rule for d²y/dx².

CalculusCommon Core CHA-3.GPARVerified correct ✓

Worked examples

A curve is defined parametrically by x = 4cos(t), y = 4sin(t). Find dy/dx using dy/dx = (dy/dt)/(dx/dt). Evaluate at t = π/3. Round to 4 decimal places.
Answer: -0.5774
A curve is defined parametrically by x = t², y = t³. Find dy/dx using dy/dx = (dy/dt)/(dx/dt). Evaluate at t = 1. Round to 4 decimal places.
Answer: 1.5

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