anonymous
  • anonymous
How do you do the derivative of f(x) = sin(x^2 + ln(x + e^x))?
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
ok here you will use the chain rule.. many times.. first the derivative of sin you will get cos(x^2 + Ln(x+e^x)
anonymous
  • anonymous
then you will multiply it by the derivative of the inside.. cos(x^2 + Ln(x+e^x) * 2x+1/x+e^x
anonymous
  • anonymous
then you will have to multiply all of that of with the derivative of ln's function so you will finally get os(x^2 + Ln(x+e^x) * 2x+(1/x+e^x ) * (1+e^x)

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anonymous
  • anonymous
keep in mind that the derivative of ln(x) is 1/x and e^x is e^x
anonymous
  • anonymous
thank you so much! really helps
anonymous
  • anonymous
no problem.. I actually just had my final exam on that course :P
anonymous
  • anonymous
mine is in 5 hours, and im getting confused with a lot of things, especially inverse trig . like intergral arctan x dx stuff like that
anonymous
  • anonymous
I could help you! im not doing anything right now.. by the way what is the name of your textbook? we might have the same one
anonymous
  • anonymous
Calculus concepts and contexts by James Stewart
anonymous
  • anonymous
I'm just really confused with acrtan, arcsin, and arccos, and how to find their derivative and antiderivative
anonymous
  • anonymous
I have james stewart book too.. but the single variable one with the violin on the cover lol... what helped me the most with these is re write everything in a tables
anonymous
  • anonymous
ya me its the 4th edition
anonymous
  • anonymous
when they ask you what is the antiderivative of 1/1+6^2 you know that its is the arctan(6) right? im just giving you a very simple example here lol
anonymous
  • anonymous
no i ddint't know that, i know that 1/1+x^2 is arccos or arcsin haha not too sure to be honest, i've never been able to grasp the concept of inverse trig.
anonymous
  • anonymous
ok its confusing I know but arcsin and arccos are exaclty the same with one - sign difference so arcsine is 1/sqrt(1-x^2) and arccos is -1/sqrt(1-x^2)
anonymous
  • anonymous
arctan is the different one its 1/1+x^2 Do you have the solution manual with your textbook? it reaaaaaally helps to solve exercises and find them in the solution manual
anonymous
  • anonymous
now just a practice exam, my prof was terrrrible to be honest.
anonymous
  • anonymous
Oh trust me.. I failed it the first time I did this course.. they are All horrible.. lol
anonymous
  • anonymous
so then would the intergral of arctan x dx, just be 1/1+x^2?
anonymous
  • anonymous
Exaaaaaaaaaaaaaaaaactly!
anonymous
  • anonymous
Btw did you find this website thru paul's online notes? cuz I was doing linear algebra when I saw your question on the side lol... linear algebra succccccks and paul's online notes for calculus are amazing
anonymous
  • anonymous
ya haha thats how i found it.
anonymous
  • anonymous
kk so if u dont mind can i ask u another question?
anonymous
  • anonymous
no sure go ahead
anonymous
  • anonymous
integral of t^2e^3t, how do i proceed? do i simplify it first?
anonymous
  • anonymous
ok well you know that the derivative of e^x is e^x and when u integrate t^2 is 1/3 t^3 right? I just find it helpful to do them speratly but just give me one sec to recheck on somthing
anonymous
  • anonymous
ya i knwo that, its because there multiplied that im confused :S
anonymous
  • anonymous
yeah thats what im checking up on lol
anonymous
  • anonymous
ok so you have to use the tabular method.. where you integrate by parts..did u ever do this in class?
anonymous
  • anonymous
i think it has to do with substitution. but dont know how to do taht yet ha. pelletty. lol
anonymous
  • anonymous
nope
anonymous
  • anonymous
im telling you ym prof was useless.
anonymous
  • anonymous
LOL ok I found a really good website to help u with it.. check it out and I'll still be here if u have Q's http://www.hyper-ad.com/tutoring/int_parts.htm
anonymous
  • anonymous
thanks man, i really appreciate it
anonymous
  • anonymous
no problem.. I know exactly how u feel lol..
anonymous
  • anonymous
how do you intergrate e^3t
anonymous
  • anonymous
its e^3t/3
anonymous
  • anonymous
everytime?, because won't the exponent increment?
anonymous
  • anonymous
well yeah,. actually... I have no idea.. but I would do it that way.. sorry man
anonymous
  • anonymous
it's cool man, uve been a good help. thnx again!
anonymous
  • anonymous
Im glad to help really good luck!

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