What does it mean when they ask: Which ONE of these functions would logarithmic differentiation truly be beneficial/necessary?
x^e^x^2
ln(x^2e^x^2)
x^2+e^x^2
x^2/e^x^2
logarithmic differentiation is used, or is beneficial when we have a variable or function as a power. for instance, we would use logarithmic differentiation to find $\displaystyle \frac d{dx}2^{x^2 + 1}$ or $\displaystyle x^{e^x + 5x^2}$ or something like that. we usually don't need logarithmic differentiation for when e is raised to some variable power