Question:
For any differentiable function y of x,
(d²x)/(dy²)((dy)/(dx))³+(d²y)/(dx²)=
For any differentiable function y of x,
(d²x)/(dy²)((dy)/(dx))³+(d²y)/(dx²)=
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Remember the relation between second derivatives of inverse functions.
Updated On: Mar 19, 2026
- \(0\)
- \(y\)
- \(-y\)
- x
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The Correct Option is A
Solution and Explanation
We know the identity:
(d²x)/(dy²) = -(d²y/dx²)/((dy/dx)³)
Substituting:
(d²x)/(dy²)((dy)/(dx))³
= -(d²y)/(dx²)
Hence, the given expression becomes:
-(d²y)/(dx²) + (d²y)/(dx²) = 0
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