Differentiation: Logarithmic vs. Basic

[jmorris1]

My question is not exactly a problem, rather it's how to determine which way to go when differentiating a function. How do I recognize when to use logarithmic differentiation when I am not explicitly told to do so? I know that for a function a^x it's derivative is equal to a^x ln x. And I know the how to figure the problems out each way, I just was wondering how to recognize when to use the 2 different styles. Thanks!

 

[fasteddie65]

You can also use logarithmic differentiation when the function is extremely complicated looking, i.e. products and/or quotients and with exponents as well.

 

[qpmathelp]

you use logarithmic differentiation

for problems with variables in the base as well as exponent(power)

for example
x^x

x^sinx

x^y = y^x

(lnx)^sinx

you can also take log before you differentiate some complicated expressions
that consists of product or quotients of terms with powers

for eg u = {(x^3) [2x+3]^5} / { (5x+7)^7}

example
http://rbmix.com/problem/math/lg/lg.html