For x>1 , if (2 x)^ 2 y =4 e^ 2 x-2 y , then (1+ 2 x)^2 d y d x is equal to

Step-by-step solution

aligned & (2 x)^ 2 y =4 e^ 2 x-2 y 2 y (2 x)= 4+2 x-2 y & 2 y (2 x)=2 2+2 x-2 y aligned Different w.r.t x aligned & d y d x (2 x)+y 1 2 x 2=0+1- d y d x & d y d x (1+ 2 x)=1- y x =1- x+ 2 x(1+ 2 x) & [ from (1) y= x+ 2 (1+ 2 x) ] & d y d x (1+ 2 x)^2= x(1+ 2 x)-x- 2 x & (1+ 2 x)^2= d y d x = x 2 x- 2 x aligned