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if $$ \begin{cases} x= 2 \cos \theta - \cos 2\theta \\ y = 2 \sin \theta - \sin 2\theta \end{cases} $$ find $d^2y/dx^2$ at $\theta = \frac{\pi}{2}$

I have solved $\frac{dy}{d\theta}$ and $\frac{dx}{d\theta}$ and from this also solved $$ \frac{dy}{dx}= \frac{\cos {\theta}-\cos{ 2\theta}}{-\sin {\theta} +\sin{2\theta}}$$

after this I am confused.

Arctic Char
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  • https://math.stackexchange.com/a/4021938/688539 – tryst with freedom Aug 17 '21 at 07:20
  • Since you have found the first derivative, you can find the second derivative by differentiating the first derivative. You will need to use the quotient and the chain rules. You can then substitute π/2 in the result. – MathGeek Aug 17 '21 at 16:41

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