If y= x 1-x and d y ~d x = m x^2+2 n x+1 , then m^2+n^2 is

Step-by-step solution

aligned & y= x 1-x & y= ⁻¹ ( x 1-x ) & d y ~d x = 1 1+ ( x 1-x )^2 d d x ( x 1-x ) & = 1 1-2 x +x^2 ^2 +x^2 ^2 (1-x )^2 & (1-x ) +(x ) (1-x )^ 2^ & = -x +x 1+2(- ) x+x^2 & = x^2+2(- )+1 & = m x^2+2 n x+1 & n =- and m = & m^2+n^2=1 & aligned