f(x)=x^5x Use logarithmic differentiation to determine the derivative.
let y = x^(5x)
ln y = ln(x^(5x))
lny = 5x lnx
y'/y = 5x(1/x) + 5lnx
y ' = y (5 + 5lnx)
= 5x^(5x) (1 + lnx)
ln y = ln(x^(5x))
lny = 5x lnx
y'/y = 5x(1/x) + 5lnx
y ' = y (5 + 5lnx)
= 5x^(5x) (1 + lnx)