If y= [ e ^ 4 x ( x-4 x+3 )^ 3 4 ] then d y ~d x =

Step-by-step solution

y=e^ 4 x ( x-4 x+3 )^ 3 4 Taking log on both sides, aligned & y= [ e ^ 4 x ( x-4 x+3 )^ 3 4 ] & y= e ^ 4 x + ( x-4 x+3 )^ 3 4 & y=4 x e + 3 4 ( x-4 x+3 ) & y=4 x+ 3 4 ( x-4 x+3 ) aligned Differentiating w.r.to x on both sides, aligned & 1 y ~d y ~d x =4+ 3 4 1 (x-4) d ~d x ( x-4 x+3 ) (x+3) & 1 y ~d y ~d x =4+ 3 4 ( x+3 x-4 ) ( (x+3)-(x-4) (x+3)^2 ) & 1 y ~d y ~d x =4+ 3 4 ( 1 x-4 ) ( x+3-x+4 (x+3) ) & 1 y ~d y ~d x =4+ 3 4 ( 1 x-4 ) ( 7 x+3 ) aligned d y ~d x =y [4+ 21 4(x-4)(x+3) ]