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Calculus II Derivative Help

abrammer12

New member
Joined
Jan 10, 2015
Messages
1
Hello all! Well this is my first post ever, so here it goes. I am taking an online Calculus II class, which leaves me with no one to ask questions for when I get confused. I think I found the solution, but got it rather easily, which makes me want to second guess myself. Any advice or help would be very much appreciated!

Problem: What is the derivative of ln(x+ln x).

My answer: 1/x(x+ln x)

Wow, so simple right? I split the problem into lnx multiplied by ln(ln x) and solved for the derivative. Being a Calculus II course, I am wondering if I was suppose to do more work.


My answer is on the multiple choice answers (which can be a trap!), but the other answers are:


b. x/x+ ln x
c. 1/x+ ln x
d. 1/x+ ln x multiplied by (1 + 1/x)

I hope to be right and questioning for no reason, but we'll see what happens. Thank you so much for the help :D:D:D:D:D:D:D
 

Ishuda

Elite Member
Joined
Jul 30, 2014
Messages
3,345
Hello all! Well this is my first post ever, so here it goes. I am taking an online Calculus II class, which leaves me with no one to ask questions for when I get confused. I think I found the solution, but got it rather easily, which makes me want to second guess myself. Any advice or help would be very much appreciated!

Problem: What is the derivative of ln(x+ln x).

My answer: 1/x(x+ln x)

Wow, so simple right? I split the problem into lnx multiplied by ln(ln x) and solved for the derivative. Being a Calculus II course, I am wondering if I was suppose to do more work.


My answer is on the multiple choice answers (which can be a trap!), but the other answers are:


b. x/x+ ln x
c. 1/x+ ln x
d. 1/x+ ln x multiplied by (1 + 1/x)

I hope to be right and questioning for no reason, but we'll see what happens. Thank you so much for the help :D:D:D:D:D:D:D
(ln(f(x))' = f'(x)/f(x)
You have the 1/f(x) [=1/(x+ln x)] correct but what about that f'(x). What is the derivative of x + ln(x)
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
2,767
Hello all! Well this is my first post ever, so here it goes. I am taking an online Calculus II class, which leaves me with no one to ask questions for when I get confused. I think I found the solution, but got it rather easily, which makes me want to second guess myself. Any advice or help would be very much appreciated!

Problem: What is the derivative of ln(x+ln x).

My answer: 1/x(x+ln x)

Wow, so simple right? I split the problem into lnx multiplied by ln(ln x) and solved for the derivative. Being a Calculus II course, I am wondering if I was suppose to do more work.
1st lets suppose that ln(x+ln(x)) = ln(x)*ln(ln(x)). This clearly is a product (even you said that you are multiply these two factor). So to get your answer did you use the product rule?.
When you take the derivative of ln of anything you always get anything'/anyhing. You have ln (x+ln(x)) so the anything is x+ln(x). The answer will be (x+ln(x))'/(x+ln(x)). So all you have to do is figure what what (x+ln(x))' is, divide it by (x+ln(x)) and clean this up.

Now back to the ln rule! ln(A) + ln(B) = ln (AB). BUT ln(x+ln(x)) does not equal ln(x)*ln(ln(x)). That is ln(A+B) is NOT ln(A)*ln(B)

To succeed in Calculus 2 you *must* know calculus 1, trigonometry, pre calculus, college algebra, basic algebra and arithmetic.
 
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Subhotosh Khan

Super Moderator
Staff member
Joined
Jun 18, 2007
Messages
18,089
Hello all! Well this is my first post ever, so here it goes. I am taking an online Calculus II class, which leaves me with no one to ask questions for when I get confused. I think I found the solution, but got it rather easily, which makes me want to second guess myself. Any advice or help would be very much appreciated!

Problem: What is the derivative of ln(x+ln x).

My answer: 1/x(x+ln x)

What you wrote actually translates to........ \(\displaystyle \frac{1}{x} * [x + ln(x)]\)

perhaps you meant:................................ \(\displaystyle \frac{1}{x * [x + ln(x)]}\)

then you should have written:.............
..1/[x(x+ln(x))]

Those
[] are very important!!

Wow, so simple right? I split the problem into lnx multiplied by ln(ln x) and solved for the derivative. Being a Calculus II course, I am wondering if I was suppose to do more work.


My answer is on the multiple choice answers (which can be a trap!), but the other answers are:


b. x/x+ ln x
c. 1/x+ ln x
d. 1/x+ ln x multiplied by (1 + 1/x)

I hope to be right and questioning for no reason, but we'll see what happens. Thank you so much for the help :D:D:D:D:D:D:D
I hope you have figured out the correct answer from other responses.
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,937
1st lets suppose that ln(x+ln(x)) = ln(x)*ln(ln(x)).
Why would one wish to suppose this? The rule for logs is that ln(a*b) = ln(a) + ln(b). It is not true that ln(x + ln(x)) equals ln(x)*ln(ln(x).

Problem: What is the derivative of ln(x+ln x).

My answer: 1/x(x+ln x)

Wow, so simple right? I split the problem into lnx multiplied by ln(ln x)...
Apologies for any confusion about the log rules. You can follow the link (above) for clarification, as needed. However, the "solution" is suggested in the first reply you received. To clarify:

Rather than trying to break the log expression into two terms, try instead to apply the Chain Rule. You have the natural log of something on the "outside"; take the derivative of that. Then multiply that result by the derivative of the "something" (which will be the x + ln(x) sum). What do you get? ;)
 
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