If y= ( 1+x 1-x )^ 1 / 4 - 1 2 ⁻¹(x) , then d y d x at x= 1 2 equals

Step-by-step solution

aligned & (d) y= 1 4 ( 1+x 1-x )- 1 2 ⁻¹ x & y= 1 4 (1+x)- 1 4 (1-x)- 1 2 ⁻¹ x & Then, d y d x = 1 4 1 (1+x) + 1 4 1 (1-x) - 1 2 1 1+x^2 & ( d y d x )_ x=1 / 2 = 1 4 1 1+1 / 2 + 1 1-1 / 2 & - 1 2 ( 1 1+1 / 2 ) & = 1 4 2 ( 2 -1)+ 2 ( 2 +1) ( 2 +1)( 2 -1) - 1 3 & aligned aligned & = 1 4 2- 2 +2+ 2 2-1 - 1 3 & =- 1 4 4 1 - 1 3 =1- 1 3 = 2 3 ( d y d x )_ x=1 / 2 & = 2 3 aligned