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AP EAMCET201923 Apr 2019Morning ShiftMathematicsDifferentiationActual

If ( (f(x))= 1-x^2 1+x^2 ) and ( (g(x))= 3 x-x^3 1-3 x^2 ), then ( d f d g = )

Options

  1. A( 3 2 )
  2. B( 1+x^2+2 x^3 (1-3 x^2 )^2 )
  3. C( 2 3 )
  4. D( x^2+x^3 (1+x^2 ) (1-3 x^2 ) )

Correct answer

C. ( 2 3 )

Step-by-step solution

Given, ( (f(x))= 1-x^2 1+x^2 ) Put ( x= ) ( aligned (f(x)) & = 1- ^2 1+ ^2 (f(x)) & = 2 f(x) & =2 =2 ⁻¹ x (g(x)) & = 3 x-x^3 1-3 x^2 aligned ) Put ( x= ) ( aligned & (g(x))= 3 - ^3 1-3 ^2 & (g(x))= 3 & g(x)=3 =3 ⁻¹ x & f^ (x) g^ (x) = 2 3 & d f d g = 2 3 aligned ) Hence, answer is (c).

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