Derivative of natural log?

Question

What's the derivative of y(x)=xln(x^2)?

Answer 1

If I remember correctly...

y'(x) = 1 ln(x^2) + x d(ln(x^2))/dx

y'(x) = 1 ln(x^2) + x (1 / x^2) d(x^2)/dx

y'(x) = 1 ln(x^2) + x (1 / x^2) 2x

y'(x) = ln(x^2) + 2x^2 / x^2

y'(x) = ln(x^2) + 2