Question

Find d/dx, please help

Answer 1

You want to find the derivative ... of what function?

Answer 2

sorry, that took a while to upload

Answer 3

You're finding the derivative of a function which is defined by an incomplete definite integral. Have you heard of the "Fundamental Theorem of Calculus?"

Answer 4

If so, do you see any application of that Theorem here?

Answer 5

yes, but I'm not sure how to use it

Answer 6

im almost clueless

Answer 7

Do you have your Calculus book open and in front of you?

Answer 8

I can open it, should I open to something specifically?

Answer 9

Fundamental Theorem of Calculus.

Answer 10

looking for it, will you stay here, to explain the rest of the question once I find it?

Answer 11

Quoting "wolframalpha.com:"

"The second fundamental theorem of calculus holds for f a continuous function on an open interval I and a any point in I, and states that if F is defined by

F(x)=int_a^xf(t)dt, "

Please look up "Fundamental Theorem of Calculus, Part 2"

or


"Second Fundamental Theorem of Calculus."

Answer 12

\[F(x)=\int\limits_a^xf(t)dt, \]

Answer 13

What is the function?

Answer 14

As definited immediately above your question.
It's a function defined as an integral where the integration has not yet been completed.

Answer 15

@anikate: What info have you found so far about this?

Answer 16

still reading through trying to understand it. can you explain it to me?

Answer 17

Not as well as the book can. Could you toss out some leading questions that I could answer? This would be more productive for you than my just starting from scratch with my own explanations.

the problem you've posted involves more than the Second Fundamental Theorem of Calculus, namely, the chain Rule. You'd have to understand the Second Theorem in its simplest form before tackling the problem you've posted.

Mind picking out one of the easier-looking problems from y our textbook under Second Fund. Thm. of Calculus?

Answer 18

Could you show me the steps to the problem? I'll understand it @mathmale

Answer 19

\[\int\limits\limits_{x}^{x^2}\ln tdt=-\int\limits\limits_{0}^{x}\ln t dt+\int\limits\limits_{0}^{x^2}\ln t dt\]

Answer 20

Your job is to find the derivative of this function.
Can you find the derivative of
\[-\int\limits_{0}^{x}\ln t dt\]
following the 2nd Fundamental Theorem of Calculus?

Answer 21

The answer is -ln x. But you must know how to obtain that yourself.

Answer 22

sorry if I'm not responding, I'm not ignoring you, just following the work

Answer 23

Are you going to be on OpenStudy tomorrow morning? I ask because I need to get off the 'Net within a few minutes.

Answer 24

its an x^3 not x^2 in the question

Answer 25

and no I won't be

Answer 26

I do need to get off the 'Net. that x^3 (instead of x^2) is a snap to handle. what you need here, I'm afraid, is actual, hands-on practice with the Second fund. Them. of Calc.
that's why I asked y ou to share a simpler problem as a focus for discussion of this Theorem.

Answer 27

If you want to finish this problem tonight (which seems to be the case), then consider posting a new question in which you ask for help in finding the derivative of \[-\int\limits_{0}^{x}\ln t dt\]

Answer 28

Next, post another question, asking for help in finding \[\int\limits_{0}^{x^2}\ln t dt\], which will require application of the Chain Rule.

Answer 29

By learning how to do these two problems separately, you will have learned how to do the problem you've posted here, \[\int\limits_{x}^{x^2}\ln t dt\]

Answer 30

so will the answer just look the derivative of those two added up? @mathmale

Answer 31

If done correctly, yes, that's it.

Don't forget the - sign in front of \[\int\limits_{0}^{x}\ln t dt\]

Answer 32

Hope to work with you again in the future. I like your attitude. Good night!

Answer 33

oh cool! thank for all the help!

Answer 34

@geerky42 can you derive those 2?