For the curve C:(x²+y²-3)+(x²-y²-1)⁵=0, the value of 3 y^()-y³ y^(), at the point (α, α), α>0, on C, is equal to _ _ _ _ _ _.

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 27 Jul, Evening shift · Q34

JEE Main 202227 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

For the curve

C:\left(x^{2}+y^{2}-3\right)+\left(x^{2}-y^{2}-1\right)^{5}=0

, the value of

3 y^{\prime}-y^{3} y^{\prime \prime}

, at the point

(\alpha, \alpha)

\alpha>0

, on C, is equal to ____________.

Your answerType your answer. Integers and decimals are accepted.