Given y = (ln 4x) ^(2x) and x greater than 1/4, find y prime (x)?

Answer 1

There is a formula you can use, but most likely the professor would like to see you use logs

so take the log of each side

lny=ln(ln(4x)^(2x))=2xln(ln4x)

now implicitly differentiate

it it will be a product til with a chain rule inside on the right, the left will be

y’/y=d/dx2xln(ln4x)

from here you should do the rest

you can plug into wolfram to verify answer