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Manipal MET2010MathematicsDifferentiation

If y= (m ⁻¹ x ) , then (1-x^2 ) y^ -x y^ is equal to

Options

  1. Am^2 y
  2. Bm y
  3. C-m^2 y
  4. DNone of these

Correct answer

C. -m^2 y

Step-by-step solution

We have, y= (m ⁻¹ x ) d y d x = (m ⁻¹ x ) m 1-x^2 aligned (1-x^2 ) ( d y d x )^2 & =m^2 ^2 (m ⁻¹ x ) & =m^2(1- ) aligned On differentiating w.r.t. x , again, we get (1-x^2 ) 2 d y d x d^2 y d x^2 + ( d y d x )^2 (-2 x)=-2 m^2 y d y d x (1-x^2 ) d^2 y d x^2 -x d y d x =-m^2 y[ Dividing by 2 d y / d x]

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