Find the derivative of f(x) = (((e^x(x^2+cos(x)))/(arctan(x)ln^5(3x^4)))^4 using logarithmic differentiation

Question

A step by step solution would be highly appreciated

Answer 1

ln y = ln e^x + ln cos x - ln arctanx - 5ln 4ln(3x^4)

y'/y = 1/e^x + sinx/cosx - 1/(1+x^2) - 5 ( 12x^3/ ln 4ln 3x^4))

y' = [ 1/e^x + sinx/cosx - 1/(1+x^2) - 5 ( 12x^3/ ln 4ln 3x^4))] y

where y is the given function