If y= ⁻¹( x+ x), then d y d x =

Step-by-step solution

Given aligned y &= ⁻¹ ( 1 x + x x )= ⁻¹ ( 1+ x x ) &= ⁻¹ [ ( ² x 2 + ² x 2 )+2 x 2 x 2 ² x 2 - ² x 2 ) &= ⁻¹ x ( x 2 + x 2 ) ( x 2 - x 2 ) &= ⁻¹ x 2 + x 2 x 2 - x 2 = ⁻¹ ( 1+ x 2 1- x 2 ) &= ⁻¹ ( ( 4 + x 2 ) ) aligned aligned y &= 4 + x 2 dy dx &=0+ 1 2 = 1 2 aligned