If $x = a\sin {\rm{\theta }}\,$ and $y = b\cos {\rm{\theta }},$ then $\frac{{{d^2}y}}{{d{x^2}}}$ is equal to

$ - \frac{b}{{{a^2}}}{\sec ^3}{\rm{\theta }}$

$\frac{a}{{{b^2}}}{\sec ^2}{\rm{\theta }}$

$ - \frac{b}{a}{\sec ^2}{\rm{\theta }}$

$\frac{b}{{{a^2}}}{\sec ^3}{\rm{\theta }}$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

x = a\sin \mathrm{\theta }\,

and

y = b\cos \mathrm{\theta },

then

\frac{{{d^2}y}}{{d{x^2}}}

is equal to

View answer and explanation

Correct option: D

- \frac{b}{{{a^2}}}{\sec ^3}\mathrm{\theta }

Option D (

- \frac{b}{{{{a^2}}}}\sec ^3\mathrm{\theta }

) is correct because it is the result of differentiating the given parametric equations twice with respect to x.

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