Question

Use logarithmic differentiation to find the derivative of f(x) = x^x+2 and simplify. Please show steps. Thanks.

Answer 1

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