If y= ⁻¹ x 1+2 x^2 + ⁻¹ x 1+6 x^2 + ⁻¹ x 1+12 x^2 , then ( d y d x )_ x= 1 2 =

Step-by-step solution

aligned & y= ⁻¹ x 1+2 x^2 + ⁻¹ x 1+6 x^2 + ⁻¹ x 1+12 x^2 & d y d x = 1-2 x^2 (1+2 x^2 )^2+x^2 + 1-6 x^2 (1+6 x^2 )^2+x^2 + 1-12 x^2 (1+12 x^2 )^2+x^2 & ( d y d x )_ x= 1 2 = 1- 1 2 (1+ 1 2 )^2+ 1 4 + 1- 3 2 (1+ 3 2 )^2+ 1 4 + 1-3 (1+3)^2+ 1 4 & ( d y d x )_ x= 1 2 = 1 5 - 1 13 - 8 65 =0 aligned