If y= ⁻¹ ( 4 2 x 2 x-6 ^2 x ) , then ( d y ~d x ) at x=0 is

Step-by-step solution

aligned & y= ⁻¹ ( 4 2 x 2 x-6 ^2 x ) & = ⁻¹ [ 4(2 x x) ( ^2 x- ^2 x )-6 ^2 x ] & = ⁻¹ ( 8 x x ^2 x-7 ^2 x ) aligned aligned & = ⁻¹ ( 8 x 1-7 ^2 x ) & = ⁻¹ ( 7 x+ x 1-7 x x ) & = ⁻¹(7 x)+ ⁻¹( x) & y= ⁻¹(7 x)+x & d y ~d x = 1 1+(7 x)^2 7 ^2 x+1 aligned gathered = 7 ^2 x 1+49 ^2 x +1 ( d y ~d x )_ x=0 = = 7 ^2 0 1+49 ^2 0 +1 = 7 1+0 +1 =8 gathered