# Instances where Logarithmic Differentiation doesn't work?

1. Oct 14, 2015

### in the rye

Hey,

In my class we just learned about logarithmic differentiation. I can see this being useful when taking the derivative of a complex function since it could be messy. But, I tried it on simpler equations as well. Everything I tried it on it seemed to work. Are there ever instances that it does not work?

To make sure we are using the same definition of logarithmic differentiation, I simply mean taking the log of both sides of an equation before taking its derivative. So where:

y = x2
ln y = ln (x2)
1 / y * y' = 1 / x2 * 2x
y' = 2y / x
y' = 2x

Certainly just taking the derivative of this is easier, but it's just an example.

2. Oct 14, 2015

### Staff: Mentor

To the best of my knowledge, no.
Your example is a very simple one, for which log differentiation is a lot more work than it would be by simpler means.

Here are some examples where log differentiation would be very useful.
1. $y = (3x^2 + 5)^{1/x}$
2. $y = (\sin x)^{x^3}$
(from https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/logdiffdirectory/LogDiff.html)