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If x4 + y4 = 16, then find the second derivative of y.

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  1. y" = 
  2. y" = 
  3. y" = 
  4. y" = 

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Option 2 : y" = 
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Detailed Solution

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Concept: 

Given:  x4 + y4 = 16

Differentiate both the sides with respect to x, we get

4x3 + 4y3 = 0

4y3  = - 4x3 

y3 = - x3  ⇒ 

Again, differentiate both the sides with respect to x, we get

⇒  (∵ )

Multiply both the sides by y4, we get

  (since y4 = 16 - x4)

Therefore the correct answer is  .

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