If y= ⁻¹ [ 1 1+x+x^2 ]+ ⁻¹ [ 1 x^2+3 x+3 ], x>0 , then d y d x =

Step-by-step solution

aligned & y= ⁻¹ [ 1 1+x+x^2 ]+ ⁻¹ [ 1 x^2+3 x+3 ] & = ⁻¹ [ 1 1+x(1+x) ]+ ⁻¹ [ 1 1+(x+2)(x+1) ] & = ⁻¹ [ (x+1)-1 1+(x+1) x) ]+ ⁻¹ [ (x+2)-(x+1) 1+(x+2)(x+1) ] & = ⁻¹( x +1)- ⁻¹( x +2)- ⁻¹( x +1) & = ⁻¹( x +2)- ⁻¹( x ) & dy dx = 1 1+( x +2)^2 - 1 1+ x ^2 & aligned