The derivative of ⁻¹ ( 1 2 x^2-1 ) with respect to 1-x^2 at x= 1 2 equals

Step-by-step solution

Let u= ⁻¹ ( 1 2 x^2-1 ) and v= 1-x^2 Put x= u= ⁻¹ ( 1 2 ^2 -1 ) and v= 1- ^2 aligned & u= ⁻¹( 2 ) and v= & u=2 and v= & d u d =2 and d v d = d u d v = d u / d d v / d = 2 aligned d u d v = 2 x [ =x] At x= 1 2 ( d u d v )_ x=1 / 2 = 2 1 / 2 =4