If y= ⁻¹ [ 1+x 2 ]+x^x , then d y d x at x=1 is

Step-by-step solution

aligned & ⁻¹ [ 1+x 2 ]+x^x & = ⁻¹ [ ( 2 - 1+x 2 ) ]+x^x & = 2 - 1+x 2 +x^x & d y d x =0- 1 2 d d x ( 1+x )+ d d x (x^x ) aligned Let u = x ^ x u = x x aligned & 1 u d u d x = x x + x d y d x =x^x(1+ x) & d y d x = -1 2 [ 1 2 1+x ]+x^x(1+ x) & [ d y d x ]_ x=1 = ( -1 2 ) ( 1 2 2 )+1= -1 4 +1= 3 4 aligned