Question

y=x^logbase5(x)

Answer 1

lny = log_5(x) lnx

= lnx/ln5 lnx
= 1/ln5 ln^2(x)

1/y y' = 1/ln5 * 2lnx * 1/x
y' = 2y lnx / x ln5
= 2lnx/ln5 x^(log_5(x)-1)
= 2log_5(x) x^(log_5(x)-1)