JEE MainMathematicsModerateDifferentiation

If a curve is represented parametrically by the equations x =
4t^3 + 3 and y = 4 + 3t^4 and
$\frac{\left( \frac{d^{2}x}{dy^{2}} \right)}{\left( \frac{dx}{dy} \right)^{n}}$
is.

Show answer and solution

\frac{dx}{dy} = \frac{\frac{dx}{dt}}{\frac{dy}{dt}} = \frac{12t^{2}}{12t^{3}} = \frac{1}{t}

\frac{d^{2}x}{dy^{2}} = \frac{d}{dy}\left( \frac{dx}{dy} \right) = \frac{d}{dt}\left( \frac{1}{t} \right) \cdot \frac{dt}{dy} = \frac{- 1}{t^{2}} \cdot \frac{1}{12t^{3}} = \frac{- 1}{12t^{5}}

\frac{\frac{- 1}{12t^{5}}}{\left( \frac{1}{t} \right)^{n}}\

is
constant

\Rightarrow

n =

Source: Grass-G / M-12 Mathematics Paper 2 Nov.docx

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