d d x (x+1)^2 x-1 (x+4)^3 e^x =f(x) [ array c 2 x+1 + 1 2(x-1) - 3 x+4 -1 array ] then f(5)=

Step-by-step solution

Let y=f(x)= (x+1)^2 x-1 (x+4)^3 e^x aligned & y= [ (x+1)^2 x-1 (x+4)^3 e^x ] & y=2 (x+1)+ 1 2 (x-1) aligned -3 (x+4)-x On differentiating both sides w.r.t. x , 1 y d y d x = 2 x+1 + 1 2(x-1) - 3 x+4 -1 aligned & d y d x =f(x) [ 2 x+1 + 1 2(x-1) - 3 x-4 -1 ] & f(x)= (x+1)^2 x-1 (x+4)^3 e^x aligned f(5)= 36 2 9^3 e^5 = 8 81 e^5