Calculus question: what is the derivative for y=x^(x+2) using logarithmic differentiation?

Question

Calculus question: finf the derivative for y=x^(x+2) using logarithmic differentiation. I am stumped. None of my homework example from my calc book match this type of problem, please help

Answer 1

y = x^(x+2); it's a function to the power of a function, so logarithmic differentiation is indeed a good idea.
ln y = (x+2) ln x
<=> 1/y dy/dx = (1) ln x + (x+2)(1/x)
<=> dy/dx = y (ln x + 1 + 2/x)
= x^(x+2).(ln x + 1 + 2/x)

Answer 2

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

ln (y) = (x + 2)*ln(x)

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

y' = y * [(x + 2)/x + ln(x)]
=x^(x+2) * [(x + 2)/x + ln(x)]