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AP EAMCET201922 Apr 2019Morning ShiftMathematicsDifferentiationActual

If (x=4 ^3 ) and (y=3 ^2 ), then ( d^2 y d x^2 ) at ( = 4 ), is

Options

  1. A( 1 3 )
  2. B( 1 6 )
  3. C( -1 6 )
  4. D( -1 3 )

Correct answer

B. ( 1 6 )

Step-by-step solution

Given, (x=4 ^3 )...(i) and (y=3 ^2 )...(ii) Differentiating Eq. (i) and Eq. (ii) w. r. t. (t ) ( aligned d x d & =4 3 ^2 (- ) & =-12 ^2 (iii) aligned ) ( aligned and d y d & =3 2 & =6 (iv) aligned ) ( aligned Now, d y d x & = d y d d x d & =- 1 2 ~[ by Eqs. (iii) and (iv)] aligned ) So, ( d^2 y d x^2 =- 1 2 d d x ) ( aligned & =- 1 2 -1 12 ^2 [by Eq. (iii)] & = 1 24 1 1 ^2 & = 1 24( )^4 = 1 24 ( 4 )^4 ( = 4 ) & = 1 24 1 ( 1 2 )^4 = 1 24 4= 1 6 aligned )

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