# Natural log derivative

#### airken

##### New member
if f(x)= 3x lnx, then f ' (x)=?

i used

f' ' (x)=3x(D lnx) + D (3x) (lnx)

f ' '(x)=3x (1/x) + 3 (lnx)

so... f ' '(x)=3+3lnx or 3(1+lnx).

unfortunately this isn't one of the possible answers given. could one of you kind folks help me understand where i went wrong?

thank you

Last edited:

#### MarkFL

##### Administrator
Staff member
Re: natural log derivative

Hello airken and welcome to MHB.

You have correctly applied the product rule, and your result is thus correct. Now, there are different ways to write this result, for example $f'(x)=\ln((ex)^3)$.

Can you list the possible choices so we can figure out which is equivalent?

edit: I see you have edited your post. You don't want to use a double-prime notation, unless you actually differentiate again. I assume you are to find the first derivative?

#### airken

##### New member
Re: natural log derivative

Wow! that was sooo fast. thank you for the help.
sorry, i should have thought to provide the answers
here they are.

a) 3+ln(x^3)
b) 1+ln(x^3)
c) (3/x)+3lnx
d) 3/(x^2)
e) 1/x

thank you again for the help
Hello airken and welcome to MHB.

You have correctly applied the product rule, and your result is thus correct. Now, there are different ways to write this result, for example $f'(x)=\ln((ex)^3)$.

Can you list the possible choices so we can figure out which is equivalent?

edit: I see you have edited your post. You don't want to use a double-prime notation, unless you actually differentiate again. I assume you are to find the first derivative?

#### MarkFL

##### Administrator
Staff member
Re: natural log derivative

Using the property $\ln(a^b)=b\cdot\ln(a)$, which one of those choices can be made to match your result?

#### airken

##### New member
Re: natural log derivative

sorry, you're right, couldn't see the first ' and thought i forgot it.
thank you for the help,
and thank you for explaining the law of logs, i was having probs with that.

i get A
and i hope my kid gets one too.

thanks again for the help

Hello airken and welcome to MHB.

You have correctly applied the product rule, and your result is thus correct. Now, there are different ways to write this result, for example $f'(x)=\ln((ex)^3)$.

Can you list the possible choices so we can figure out which is equivalent?

edit: I see you have edited your post. You don't want to use a double-prime notation, unless you actually differentiate again. I assume you are to find the first derivative?

#### MarkFL

##### Administrator
Staff member
Yes, good work! A is the correct choice as:

$3+3\ln(x)=3+\ln(x^3)$

You did very well in presenting your problem, and you showed your work which made it easy to give help.

#### HallsofIvy

##### Well-known member
MHB Math Helper
if f(x)= 3x lnx, then f ' (x)=?

i used

f' ' (x)=3x(D lnx) + D (3x) (lnx)

f ' '(x)=3x (1/x) + 3 (lnx)

so... f ' '(x)=3+3lnx or 3(1+lnx).

unfortunately this isn't one of the possible answers given. could one of you kind folks help me understand where i went wrong?

It is just a matter of notation but this is not f'', the second derivative of f.

Did the problem ask you to find f' or f''?

[quore]thank you
[/QUOTE]

#### airken

##### New member
Hi Halls of Ivy,

thank you for taking the time to look at my post. this is an older post, i think about 3.5 years ago and MarkFl was kind enough to help me with it originally.
to your question, unfortunately i've forgotten all about this one, and couldn't tell you if i might have made a mistake when typing in the original question.

kid is now a junior at cal poly san luis obispo (computer engineering), and far beyond any math help i can give anymore.

thank you again to you and all here for your most generous time and efforts.