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AP EAMCET20225 Jul 2022Morning ShiftMathematicsDifferentiationActual

If x=f( ) and y=g( ) , then d^2 y d x^2 =

Options

  1. Ag^ ( ) f^ ( )
  2. Bf^ ( ) x( )
  3. Cf^ ( ) g^ ( )-g^ ( ) f^ ( ) (f^ ( ) )^3
  4. Dg^ ( ) f^ ( )-g^ ( ) f^ ( ) (g^ ( ) )^3

Correct answer

C. f^ ( ) g^ ( )-g^ ( ) f^ ( ) (f^ ( ) )^3

Step-by-step solution

Given, x=f( ) and y=g( ) d x d =f^ ( ), d y d =g^ ( ) d y d x = g^ ( ) f^ ( ) aligned & d^2 y d x^2 = ( g^ ( ) f^ ( )-f^ ( ) g^ ( ) (f^ ( )^2 ) ) d d x & d^2 y d x^2 = ( g^ ( ) f^ ( )-f^ ( ) g^ ( ) (f^ ( ) )^3 ) aligned

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