A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Compute \(f'\left(0\right)\). $$\large f\left(x\right) = \int\limits_{\cos x}^{\sin x} e^{t^2+xt}dt.$$
anonymous
 4 years ago
Compute \(f'\left(0\right)\). $$\large f\left(x\right) = \int\limits_{\cos x}^{\sin x} e^{t^2+xt}dt.$$

This Question is Closed

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3Leibnitz rullllllleeeeeeeeeeeeeeeeee!!!!!!!!

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3\[\frac{\int\limits_{h(x)}^{g(x)}f(t).dt}{dx}= f(g(x)).g'(x)  f(h(x)).h'(x)\] Here, \(f(t) = e^{t^2 + xt}, g(x)=\sin x\text{ and }h(x)=\cos x\)

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3\[f'(x) = e^{\sin^2 x + x\sin x}.\cos x + e^{\cos^2 x + x\cos x}.\sin x \] \[SOoooooOOOOoooooo,~ f'(0) = e^0+ 0 = \boxed{1}\]

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3(i.e., if I did not make a characteristically stupid error again _)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Read the question again apoorv. $$\large e^{t^2 + xt}$$

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3I 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..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0No, you are differentiating with respect to \(x\).

apoorvk
 4 years ago
Best ResponseYou've already chosen the best response.3Well 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.
Ask your own question
Sign UpFind more explanations on OpenStudy
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
 Engagement 19 Mad Hatter
 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.