derivative of f(x) = 3x-1/x+2, x ≠ 2 using first principles

[kais]

Hey guys, im trying to teach myself derivatives and im stuck on a question which is Find the derivative of f(x) = 3x−1/x+2, x ≠ 2 using first principles.


Now im not sure if i use the quotient rule to work it out or if i have to do it some other way. would i write it out as

​

d/dx(3x-1/x+2)


= (x+2) · d/dx(3x-1) - d/dx(x+2) ·(3x-1)

(x+2)^2​

or am i on the wrong track?

cheers in advanced

 

[ksdhart]

What you've posted so far is absolutely correct. Well done! Is there a particular reason you're doubting your answer? Once you've memorized the quotient rule, it's largely a matter of what's sometimes called "plug-n-chug."

 

[Deleted member 4993]

What you've posted so far is absolutely correct - except for use of grouping symbols.

To make sense mathematically (and to get full credit in exams) - you must include those pesky things using principle of PEMDAS.

 

[stapel]

Find the derivative of f(x) = 3x−1/x+2, x ≠ 2 using first principles.

What does your book mean by "first principles"? (Most books mean something like "using the limit definition", which you're not doing, is why I'm asking.) Thank you!

 

[kais]

ksdhart

What you've posted so far is absolutely correct. Well done! Is there a particular reason you're doubting your answer? Once you've memorized the quotient rule, it's largely a matter of what's sometimes called "plug-n-chug."

Well im basically teaching myself this stuff, so i haven't actually worked out a division derivative yet and i wanted to check i was doing it right before i start doing all of them like it


​

Subhotosh Khan

What you've posted so far is absolutely correct - except for use of grouping symbols.

To make sense mathematically (and to get full credit in exams) - you must include those pesky things using principle of PEMDAS.

what would be the best way to write it out?



stapel

Originally Posted by kais
Find the derivative of f(x) = 3x−1/x+2, x ≠ 2 using first principles.



What does your book mean by "first principles"? (Most books mean something like "using the limit definition", which you're not doing, is why I'm asking.) Thank you! :wink:

Im learning off of internet resources, and it does say about limits in the first principles section. Im not sure how to put a limit on it, but isnt it mostly you want to go closer to 0 as in h->0 to get a much more accurate answer?



Thankyou everyone for your help!​

​

 

[stapel]

Find the derivative of f(x) = 3x−1/x+2, x ≠ 2 using first principles.

What does your book mean by "first principles"? (Most books mean something like "using the limit definition"....)

I'm learning off of internet resources, and it does say about limits in the first principles section. Im not sure how to put a limit on it....

Um... You really do kinda need to learn about that limit stuff. I would strongly suggest that you take a break and work on that for a while. You can start with Paul's Online Math Notes (here), an excellent resource. You may also find helpful Paul's article on how to study math (here).

To find the derivative "using first principles", as this exercise requires, you will need to start from here:

. . . . .\(\displaystyle \displaystyle \lim_{h\, \rightarrow\, 0}\, \dfrac{\left(\dfrac{3(x\, +\, h)\, -\, 1}{(x\, +\,h)\, +\, 2}\right)\, -\, \left(\dfrac{3x\, -\, 1}{x\, +\, 2}\right)}{h}\)