How do I evaluate the derivative of G(x) for my Calc 2 final tomorrow?

In summary, the user is asking for urgent help with evaluating the derivative of a function that involves an integral. They have tried using substitution and a Taylor series, but are unsure if they have the correct answer. Other users have provided hints and confirmed that the answer is sin(x2) - 2x*sin(x4).
  • #1
calchelp
11
0
calc 2 final tomorrow need urgent help!

Evaluate the derivative of the function

G(x) = ({integral} from x to x^2) of sin(-t^2)dt

this was on my review for the final and i just cannot get an answer. any help will be greatly appreciated.
 
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  • #2
need help evaluating derivative of sin(x^2)

sorry I'm new to this site.
i tried substitution which did not get me anywhere.

next, i did taylor series but could not get an answer.

now i am stuck. i am almost positive i have to use a taylor series.

with the series i got

x^2 - (x^6)/3! + (x^10)/5! ...

i plugged in x^2 for x
and i plugged in x for x and subtracted the two and got another series...
now what? antidifferentiate the series and say that that is my answer or did i mess up somewhere?
 
  • #3
Welcome to PF!

Hi calchelp! Welcome to PF! :smile:

(have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
calchelp said:
Evaluate the derivative of the function

G(x) = ({integral} from x to x^2) of sin(-t^2)dt

this was on my review for the final and i just cannot get an answer. any help will be greatly appreciated.

Hint: fundamental theorem of calculus. :wink:
 
  • #4


can i change the title of this thread??
 
  • #5


is the answer:

sin(-x^4)2x - sin(-x^3)
 
  • #6
calchelp said:
is the answer:

sin(-x^4)2x - sin(-x^3)

Almost … where did your x3 come from? :confused:
 
  • #7


ok... so after about 20 minutes of looking at it i realized that i completely made up the x^3 i don't know why or where it came from...

so is the answer:
sin(-x^4)2x - sin(-x^2)

please tell me that is right. i am about to go insane!
 
  • #8


can anyone confirm this please?
 
  • #9


calchelp said:
ok... so after about 20 minutes of looking at it i realized that i completely made up the x^3 i don't know why or where it came from...

so is the answer:
sin(-x^4)2x - sin(-x^2)

please tell me that is right. i am about to go insane!

That's right.
 
  • #10


thank you! dick and tiny-tim!
 
  • #11


Essentially this is using the chain rule whereby when:

G(x) = (integral of f1(x) to f2(x) ) g(t) dt

G'(x) = g(f2(x))*f2'(x) - g(f1(x))*f1'(x)

so in your case, G'(x) = sin(-x^4)*2x - sin(-x^2)
 
  • #12
Hi calchelp! :smile:

(just got up :zzz: …)
calchelp said:
so is the answer:
sin(-x^4)2x - sin(-x^2)

You can tidy it up a bit by taking the minus out of the sin (because sin(-θ) = -sinθ) …

sin(x2) - 2x*sin(x4) :wink:
 

FAQ: How do I evaluate the derivative of G(x) for my Calc 2 final tomorrow?

What topics should I focus on for my Calc 2 final?

For your Calc 2 final, it is important to review all of the major topics covered throughout the course. This includes integration techniques, applications of integration, series and sequences, and parametric and polar equations.

How can I prepare effectively for my Calc 2 final?

To prepare for your Calc 2 final, it is important to review all of your notes, textbook examples, and practice problems. You can also attend review sessions, work with a study group, and complete practice exams to help solidify your understanding of the material.

What are some common mistakes to avoid on the Calc 2 final?

Some common mistakes to avoid on the Calc 2 final include not showing all of your work, not checking your answers, and not practicing enough problems. It is also important to make sure you understand the concepts rather than just memorizing formulas.

How can I improve my problem-solving skills for the Calc 2 final?

To improve your problem-solving skills for the Calc 2 final, it is important to practice as many problems as you can. Make sure to review the steps and thought process behind each solution, and try to understand the underlying concepts rather than just memorizing formulas.

What resources are available to help me with my Calc 2 final?

There are many resources available to help you with your Calc 2 final, including online tutorials, study guides, and review books. Your professor or TA may also offer office hours or review sessions where you can ask questions and get additional help.

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