A) \[\frac{1}{{{(dy/dx)}^{2}}}\]
B) \[\frac{\left( {{d}^{2}}y/d{{x}^{2}} \right)}{{{\left( dy/dx \right)}^{2}}}\]
C) \[\frac{{{d}^{2}}y}{d{{x}^{2}}}\]
D) \[\frac{\left( -{{d}^{2}}y/d{{x}^{2}} \right)}{{{\left( dy/dx \right)}^{2}}}\]
Correct Answer: D
Solution :
\[\frac{{{d}^{2}}x}{d{{y}^{2}}}=\frac{d}{dy}\,\left( \frac{dx}{dy} \right)=\frac{d}{dy}\left( \frac{1}{\frac{dy}{dx}} \right)=\frac{-1}{{{\left( \frac{dy}{dx} \right)}^{2}}}\,.\,\frac{{{d}^{2}}y}{d{{x}^{2}}}\].
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