Using logarithmic differentiation to find the derivative of the function $y=x^{x+1}(x+1)^x$

Question

Using logarithmic differentiation, find the derivative of the function $y=x^{x+1}(x+1)^x$.

I knew one may begin with this step. $$\ln(y)=\ln(x^{x+1})+\ln(x+1)^x$$ But how to differentiate this?

Answer 1

$ln(y)=ln(x^{x+1})+ln((x+1)^x)=(x+1)ln(x)+xln(x+1)$ by logarithm rules. Then you can just use the product rule to finish it up