Limit Continuity And Differentiability Ques 6
- $\frac{d^2 x}{d y^2}$ equals
(2007, 3M)
(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) $\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-2}$
(d) $-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}$
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Answer:
Correct Answer: 6.(d)
Solution: (d) Since, $\quad \frac{d x}{d y}=\frac{1}{d y / d x}=\left(\frac{d y}{d x}\right)^{-1}$
$\Rightarrow \quad \frac{d}{d y}\left(\frac{d x}{d y}\right)=\frac{d}{d x}\left(\frac{d y}{d x}\right)^{-1} \frac{d x}{d y}$
$\Rightarrow \quad \frac{d^2 x}{d y^2}=-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-2}\left(\frac{d x}{d y}\right)=-\left(\frac{d^2 y}{d x^2}\right)\left(\frac{d y}{d x}\right)^{-3}$
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