Differentiate with respect to x: y=xln(x)

Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u () (where ' denotes the derivative) Applying this rule to our example: y=xlnx. Then we can denote u=x, v=ln(x) Hence: u'=1 v'=1/x Applying (), we have u'v=ln(x) , v'u=1 Giving y'=ln(x)+1