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

- anonymous

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

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- 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

then you will multiply it by the derivative of the inside.. cos(x^2 + Ln(x+e^x) * 2x+1/x+e^x

- 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

keep in mind that the derivative of ln(x) is 1/x and e^x is e^x

- anonymous

thank you so much! really helps

- anonymous

no problem.. I actually just had my final exam on that course :P

- 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

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

Calculus concepts and contexts by James Stewart

- anonymous

I'm just really confused with acrtan, arcsin, and arccos, and how to find their derivative and antiderivative

- 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

ya me its the 4th edition

- 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

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

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

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

now just a practice exam, my prof was terrrrible to be honest.

- anonymous

Oh trust me.. I failed it the first time I did this course.. they are All horrible.. lol

- anonymous

so then would the intergral of arctan x dx, just be 1/1+x^2?

- anonymous

Exaaaaaaaaaaaaaaaaactly!

- 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

ya haha thats how i found it.

- anonymous

kk so if u dont mind can i ask u another question?

- anonymous

no sure go ahead

- anonymous

integral of t^2e^3t, how do i proceed? do i simplify it first?

- 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

ya i knwo that, its because there multiplied that im confused :S

- anonymous

yeah thats what im checking up on lol

- anonymous

ok so you have to use the tabular method.. where you integrate by parts..did u ever do this in class?

- anonymous

i think it has to do with substitution. but dont know how to do taht yet ha. pelletty. lol

- anonymous

nope

- anonymous

im telling you ym prof was useless.

- 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

thanks man, i really appreciate it

- anonymous

no problem.. I know exactly how u feel lol..

- anonymous

how do you intergrate e^3t

- anonymous

its e^3t/3

- anonymous

everytime?, because won't the exponent increment?

- anonymous

well yeah,. actually... I have no idea.. but I would do it that way.. sorry man

- anonymous

it's cool man, uve been a good help. thnx again!

- anonymous

Im glad to help really good luck!

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