For the parametric curve x = t^2, y = t, which of the following is dy/dx in terms of t (t ≠ 0)?

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Multiple Choice

For the parametric curve x = t^2, y = t, which of the following is dy/dx in terms of t (t ≠ 0)?

Explanation:
In parametric form, the slope dy/dx is found by taking the ratio of the derivatives with respect to t: dy/dx = (dy/dt) / (dx/dt). For x = t^2 and y = t, we have dy/dt = 1 and dx/dt = 2t. Therefore dy/dx = 1/(2t), valid since t ≠ 0. This matches how the x-derivative in the denominator is 2t, not t or a constant, so the correct expression in terms of t is 1/(2t).

In parametric form, the slope dy/dx is found by taking the ratio of the derivatives with respect to t: dy/dx = (dy/dt) / (dx/dt). For x = t^2 and y = t, we have dy/dt = 1 and dx/dt = 2t. Therefore dy/dx = 1/(2t), valid since t ≠ 0. This matches how the x-derivative in the denominator is 2t, not t or a constant, so the correct expression in terms of t is 1/(2t).

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