Differentiation Question 376
Question: $ \frac{d^{2}x}{dy^{2}} $ is equal to
[AMU 2001]
Options:
A) $ \frac{1}{{{(dy/dx)}^{2}}} $
B) $ \frac{( d^{2}y/dx^{2} )}{{{( dy/dx )}^{2}}} $
C) $ \frac{d^{2}y}{dx^{2}} $
D) $ \frac{( -d^{2}y/dx^{2} )}{{{( dy/dx )}^{2}}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \frac{d^{2}x}{dy^{2}}=\frac{d}{dy}( \frac{dx}{dy} )=\frac{d}{dy}( \frac{1}{\frac{dy}{dx}} )=\frac{-1}{{{( \frac{dy}{dx} )}^{2}}}.\frac{d^{2}y}{dx^{2}} $ .
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