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

2 Answers
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

15
May 9, 2017

Answer:

Derivative of ln(3x) is #1/3x*3# or #1/x# because both 3s
cancel each other.

Explanation:

#d/dx ln(3x)# = #1/3x d/dx(3x)#
#d/dx ln(3x)# = #1/3x * 3#
#d/dx ln(3x)# = #1/x#
This is your final answer.

Was this helpful? Let the contributor know!
1500
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

5
Oct 3, 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#

Was this helpful? Let the contributor know!
1500
Impact of this question
Answer impact map
13254 views around the world
You can reuse this answer
Creative Commons License