How do you do the derivative of f(x) = sin(x^2 + ln(x + e^x))?

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How do you do the derivative of f(x) = sin(x^2 + ln(x + e^x))?

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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)
then you will multiply it by the derivative of the inside.. cos(x^2 + Ln(x+e^x) * 2x+1/x+e^x
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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keep in mind that the derivative of ln(x) is 1/x and e^x is e^x
thank you so much! really helps
no problem.. I actually just had my final exam on that course :P
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
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
Calculus concepts and contexts by James Stewart
I'm just really confused with acrtan, arcsin, and arccos, and how to find their derivative and antiderivative
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
ya me its the 4th edition
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
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.
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)
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
now just a practice exam, my prof was terrrrible to be honest.
Oh trust me.. I failed it the first time I did this course.. they are All horrible.. lol
so then would the intergral of arctan x dx, just be 1/1+x^2?
Exaaaaaaaaaaaaaaaaactly!
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
ya haha thats how i found it.
kk so if u dont mind can i ask u another question?
no sure go ahead
integral of t^2e^3t, how do i proceed? do i simplify it first?
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
ya i knwo that, its because there multiplied that im confused :S
yeah thats what im checking up on lol
ok so you have to use the tabular method.. where you integrate by parts..did u ever do this in class?
i think it has to do with substitution. but dont know how to do taht yet ha. pelletty. lol
nope
im telling you ym prof was useless.
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
thanks man, i really appreciate it
no problem.. I know exactly how u feel lol..
how do you intergrate e^3t
its e^3t/3
everytime?, because won't the exponent increment?
well yeah,. actually... I have no idea.. but I would do it that way.. sorry man
it's cool man, uve been a good help. thnx again!
Im glad to help really good luck!

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