Evaluating $\frac{d^2y}{dx^2}$ I want to evaluate $\frac{d^2y}{dx^2}$ from the given data: $x=a\cos^3\theta$ and $y=b\sin^3\theta$.
I tried in this way- $\frac{x^2}{a^2}+\frac{y^2}{b^2}=\cos^6\theta+\sin^6\theta=1-3(\frac{xy}{ab})^\frac{2}{3}$. After that I seem to be lost and will appreciate some help in doing this efficiently.

$\displaystyle x=a\cos^3\theta \Rightarrow \frac {dx}{d\theta}=-3a\cos^2\theta\sin\theta$
$\displaystyle y=b\sin^3\theta \Rightarrow \frac {dy}{d\theta}=3b\sin^2\theta\cos\theta$
$\displaystyle \Rightarrow\frac {dy}{dx}=\frac{\frac {dy}{d\theta}}{\frac {dx}{d\theta}}=\frac{3b\sin^2\theta\cos\theta}{-3a\cos^2\theta\sin\theta}=-\frac b a \tan\theta$
$\displaystyle \Rightarrow \frac{d^2y}{dx^2}=-\frac b a \sec^2\theta=-\frac b a (\frac a x)^\frac 3 2=-\frac {\sqrt a b} {\sqrt{x^3}}$ 
