calculus
posted by John .
y = (ln x)^(cos4x)
Use logarithmic differentiation to find the derivative of the function.

lny = ln[(lnx)^(cos(4x))]
= cos(4x) * ln(ln(x))
y'/y = cos(4x)*1/ln(x) * 1/x + ln(ln(x))(4sin(4x)
y' = (ln x)^(cos4x) [cos(4x)*1/ln(x) * 1/x + ln(ln(x))(4sin(4x) ]