NDA Mathematics Question (2025) — Solution

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