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NDA2025MathematicsDifferentiationActual

For the following three (03) items: Let y = f(x) = x ⁻¹ x 1 - x^2 + 1 - x^2 . If x = , then what is dy dx equal to?

Options

  1. A^2
  2. B^3
  3. C2 + ^2

Correct answer

C. 2 + ^2

Step-by-step solution

Given y = x ⁻¹ x 1 - x^2 + 1 - x^2 Substitute x = into the expression for y : y = 1 - ^2 + 1 - ^2 y = + ( ) y = + ( ) Differentiating y with respect to : dy d = d d ( ) + d d ( ( )) dy d = ( + ^2 ) + 1 (- ) dy d = + ^2 - = ^2 Differentiating x = with respect to : dx d = Using the chain rule to find dy dx : dy dx = dy d dx d = ^2 dy dx = ^3

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