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AP EAMCET202017 Sep 2020Evening ShiftMathematicsDifferentiationActual

( d d x ( ⁻¹ ( 4 x^3 27 -x ) )= )

Options

  1. A( 3 9-x^2 )
  2. B( 1 9-x^2 )
  3. C( -3 9-x^2 )
  4. D( -1 9-x^2 )

Correct answer

C. ( -3 9-x^2 )

Step-by-step solution

Let, ( aligned & y= ⁻¹ ( 4 x^3 27 -x ) & = ⁻¹ (4 ( x 3 )^3-3 ( x 3 ) ) aligned ) Let ( x 3 = A ) then, (A= ⁻¹ x 3 ) Also, ( aligned y & = ⁻¹ (4 ^3 A-3 A ) & = ⁻¹( 3 A) & =3 A=3 ⁻¹ ( x 3 ) aligned ) ( aligned d y d x & = d d x 3 ⁻¹ ( x 3 ) & =3 -1 1- ( x 3 )^2 d d x ( x 3 ) & =3 -3 9-x^2 1 3 =-3 / 9-x^2 aligned )

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