How would logarithmic differentiation be used to find the derivative of this function?

Question

f(x) = (((e^x(x^2+cos(x)))/(arctan(x)ln^5(3x^4)))^4

Answer 1

If you let y = f(x), then ln(y) = ln(f(x)). Now, use the properties of logarithms in order to simplify ln(f(x)). We then take the derivative of both sides using the chain rule, and solve for y'. These types of problems can be fairly tedious, so take it one step at a time and take it slow!