derivative of function!!!!!!!!!!!!!!!

Question

f(x)=xlnx-x

Answer 1

Given that f(x) = xlogx - x = y

Differentiating on both sides we get,

                   dy/dx = d/dx(xlogx - x)

                             = d/dx(xlogx) - dx/dx            

                             = xd/dx(logx) + logxd/dx(x) - 1    [Product rule d/dx(uv) = uv' + vu' and d/dx(x) = 1]

                             = x(1/x) + logx(1) - 1                  [Since d/dx(logx) = 1/x and d/dx(x) = 1]

                             = 1 + logx - 1

                             = logx

Therefore dy/dx = logx