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NDA2017MathematicsDifferentiationActual

What is d^2 x d y^2 equal to?

Options

  1. A- ( d^2 y d x^2 )⁻¹ ( d y d x )⁻³
  2. B( d^2 y d x^2 )⁻¹ ( d y d x )⁻²
  3. C- ( d^2 y d x^2 ) ( d y d x )⁻³
  4. D( d^2 y d x^2 )⁻¹

Correct answer

C. - ( d^2 y d x^2 ) ( d y d x )⁻³

Step-by-step solution

Let y = f ( x ) dy dx = f ^1( x ) dx dy = 1 f ^ ( x ) aligned & d^2 x d y^2 = -d d y f^ (x) (f^ (x) )^2 ...(i) & -d d y f^ (x) (f^ (x) )^2 = -d d y ( d y d x ) d x d x (f^ (x) )^2 = -d d x (f^ (x) ) d x d y ( d y d x )^2 & -f^ (x) d x d y ( d y d x )^2 = - ( d^2 y d x^2 ) ( d y d x )^3 = -d^2 y d x^2 ( d y d x )⁻³ aligned

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