The derivative of y= ⁻¹ ( 1+x - 1-x 2 ) is

Step-by-step solution

y= ⁻¹ ( 1+x - 1-x 2 ) Put, x= 2 2 = ⁻¹ x aligned & = 1 2 ⁻¹ x & = ⁻¹ ( 1+ 2 - 1- 2 2 ) & = ⁻¹ ( 2 - 2 2 ) & = ⁻¹ ( - 2 ) & = ⁻¹ ( 1 2 - 1 2 ) & = ⁻¹ ( 4 - 4 ) & = ⁻¹ [ ( 4 - ) ]= 4 - y & = 4 - 1 2 ⁻¹ x aligned Now, differentiate w.r.t ' x ', on both sides d y d x =0- 1 2 -1 1-x^2 d y d x = 1 2 1-x^2 Hence, option (4) is correct.