Find the value of k if d d x 2 2+ 2+ 2+2 (4 x) =k ( x 2 ) ( x 2 )

Step-by-step solution

aligned & Let y= 2 2+ 2+ 2+2 4 x & 1+ 2 A=2 ^2 A & y= 2 2+ 2+ 2(1+ 4 x) & = 2 2+ 2+ 4 ^2 2 x = 2 2+ 2+2 2 x & = 2 2+ 2(1+ 2 x) = 2 2+ 4 ^2 x & = 2 2+2 x = 2 2(1+ x) & y= 2 4 ^2 x 2 & aligned gathered y= 2 2 x 2 y= x 2 gathered Differentiate w.r.t. x , d y d x = x 2 x 2 ( 1 2 ) [using chain rule] Now, according to the question, aligned d y d x & =k x 2 x 2 x 2 x 2 1 2 & =k x 2 x 2 k & =1 / 2 aligned