$x = {\rm{cos\theta }},y = \sin 5{\rm{\theta }} \Rightarrow \left( {1 - {x^2}} \right)\frac{{{d^2}y}}{{d{x^2}}} - x\frac{{dy}}{{dx}}$ is

JEE MATHEMATICS MCQ: DIFFERENTIATION

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x = \mathrm{cos\theta },y = \sin 5\mathrm{\theta } \Rightarrow \left( {1 - {x^2}} \right)\frac{{{d^2}y}}{{d{x^2}}} - x\frac{{dy}}{{dx}}

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Correct option: D

- 25y

Option D (-25y) is correct because after finding the first and second derivatives and substituting, the expression simplifies to -25y.

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