Q25 / 66 · JEE Advanced 2007 (Paper 2) · Mathematics
$\frac{d^2 x}{d y^2}$ equals
- A$\left(\frac{d^2 y}{d x^2}\right)^{-1}$
- B$-\left(\frac{d^2 y}{d x^2}\right)^{-1}\left(\frac{d y}{d x}\right)^{-3}$
- C$\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-2}$
- Correct answerD$-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}$
Solution
Since,
$$
\begin{aligned}
\Rightarrow \quad \frac{d}{d y}\left(\frac{d x}{d y}\right) & =\frac{d}{d x}\left(\frac{d y}{d x}\right)^{-1} \frac{d x}{d y} \\
\frac{d^2 x}{d y^2} & =-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-2}\left(\frac{d x}{d y}\right) \\
& =-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}
\end{aligned}
$$
Hence, the correct answer is option: 'D'.