×

Hello! Socratic's Terms of Service and Privacy Policy have been updated, which will be automatically effective on October 6, 2018. Please contact hello@socratic.com with any questions.

What is the derivative of # ln(3x)#?

1 Answer
Oct 2, 2016

#ln(3x)=y#

#e^y=3x#

Now use implicit differentiation. Remember that:

#dy/dy*dy/dx=dy/dx#

If you use implicit differentiation...

#e^y=3x#

Should transform into...

#e^y*dy/dx=3#

Therefore:

#dy/dx=3/e^y#

#dy/dx=3/(3x)#

#dy/dx=1/x#


You could also differentiate it like this...

#y=ln(3x)#

#y=ln(3)+ln(x)#

*Because of logarithmic rules.

#:. dy/dx=1/x#