Question

use logarithmic differentiation to find dy/dx for y=13(x^ln(x))

Answer 1

take the ln of both sides,
ln y = ln ( 13 x^ln x ) , and then take derivative of both sides
so left side is y'/y , and right side, first add logs
ln 13 + ln (x ^ln x) = ln 13 + ln x * ln x

Answer 2

y'/y = 0 + 2ln x *1/x

Answer 3

y' = 2ln x *1/x * y = 2 ln x * 1/x * 13 ( x ^ln x )

Answer 4

thanks