Parametric, Polar & Vectors · Parametric Curves
Parametric Derivative (dy/dx)
The slope of a parametric curve x = x(t), y = y(t) is the ratio of the derivatives with respect to the parameter t.
- 2 worked examples
- 12 in Parametric, Polar & Vectors
Worked examples
- dx/dt = 2t, dy/dt = 3t²
- dy/dx = 3t²/(2t) = 3t/2
- At t = 1: dy/dx = 3/2
Answer: 3/2
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Common questions
What is the Parametric Derivative (dy/dx)?
The slope of a parametric curve x = x(t), y = y(t) is the ratio of the derivatives with respect to the parameter t. It is one of the parametric, polar & vectors formulas in the CalcRef reference.
When does the Parametric Derivative (dy/dx) apply?
The Parametric Derivative (dy/dx) holds under this condition: x'(t) ≠ 0.
How do you use the Parametric Derivative (dy/dx)?
Worked example. Find dy/dx for x = t², y = t³ at t = 1. dx/dt = 2t, dy/dt = 3t². dy/dx = 3t²/(2t) = 3t/2. At t = 1: dy/dx = 3/2. Answer: 3/2.
Practice
Quiz yourself on Parametric, Polar & Vectors
Parametric Derivative (dy/dx) is one of 12 Parametric, Polar & Vectors formulas in CalcRef, out of 136 in the library. Today's free round is 10 mixed multiple-choice questions drawn from the same dataset as this page, refreshed every day and replayable as often as you like - no account needed.