Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Ishaan94

Compute \(f'\left(0\right)\). $$\large f\left(x\right) = \int\limits_{\cos x}^{\sin x} e^{t^2+xt}dt.$$

  • one year ago
  • one year ago

  • This Question is Closed
  1. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    Leibnitz rullllllleeeeeeeeeeeeeeeeee!!!!!!!!

    • one year ago
  2. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    \[\frac{\int\limits_{h(x)}^{g(x)}f(t).dt}{dx}= f(g(x)).g'(x) - f(h(x)).h'(x)\] Here, \(f(t) = e^{t^2 + xt}, g(x)=\sin x\text{ and }h(x)=\cos x\)

    • one year ago
  3. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    \[f'(x) = e^{\sin^2 x + x\sin x}.\cos x + e^{\cos^2 x + x\cos x}.\sin x \] \[SOoooooOOOOoooooo,~ f'(0) = e^0+ 0 = \boxed{1}\]

    • one year ago
  4. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    (i.e., if I did not make a characteristically stupid error again -_-)

    • one year ago
  5. Ishaan94
    Best Response
    You've already chosen the best response.
    Medals 0

    Read the question again apoorv. $$\large e^{t^2 + xt}$$

    • one year ago
  6. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    I am sorry, but isn't that 'x' supposed to be taken as a constant when you integrate wrt to 't'?? I can't figure out where am going wrong. Or may be I do..

    • one year ago
  7. Ishaan94
    Best Response
    You've already chosen the best response.
    Medals 0

    No, you are differentiating with respect to \(x\).

    • one year ago
  8. apoorvk
    Best Response
    You've already chosen the best response.
    Medals 3

    Well that's the later part of the thing, but when am integrating, 'x' is a constant wrt 't', no balls with that. After am done the integration thingy, I am supposed to put in limits, and BAZINGA! the function is now in terms of 'x' completely. NOW we differentiate. We could follow all these steps, except that it would take ages for me to integrate that thing. So, Leibnitz to the rescue. Either this, or am missing your whole point.

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.