Differentiate [ x.ln(x)] with respect to x

The product rule is used to differentiate this since we are trying to differentiate the product of 2 parts--x and ln(x)So using the product rule which is d/dx=u.(dv/dx) +v.(du/dx)let u=x and v=ln(x)then du/dx=1 and dv/dx=1/x
So, d/dx[x.ln(x)]= x . 1/x + ln(x).1d/dx[x.ln(x)]=1 +ln(x)=ln(x) +1