A curve is represented parametrically by the equations x = f ( t )= a ^ ( b ^ t ) and y =…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
A curve is represented parametrically by the equations \(\mathrm{x}=\mathrm{f}(\mathrm{t})=\mathrm{a}^{\ln \left(\mathrm{b}^{\mathrm{t}}\right)}\)and \(\mathrm{y}=\mathrm{g}(\mathrm{t})=\mathrm{b}^{-\ln \left(\mathrm{a}^{\mathrm{t}}\right)}\)a, b > 0 and a ≠ 1, b ≠ 1 where t ∈ R.
Which of the following is not a correct expression for \(\frac{\mathrm{dy}}{\mathrm{dx}}\)?
- \(\frac{-1}{f(t)^{2}}\)
- – (g (t))2
- \(\frac{-\mathrm{g}(\mathrm{t})}{\mathrm{f}(\mathrm{t})}\)
- \(\frac{-\mathrm{f}(\mathrm{t})}{\mathrm{g}(\mathrm{t})}\)
Answer
(D) - f ( t ) g ( t )
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