Question

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

Answer 1

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)

Answer 2

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

Answer 3

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)

Answer 4

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

Answer 5

thank you so much! really helps

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

Calculus concepts and contexts by James Stewart

Answer 10

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

Answer 11

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

Answer 12

ya me its the 4th edition

Answer 13

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

Answer 14

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.

Answer 15

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)

Answer 16

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

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

Exaaaaaaaaaaaaaaaaactly!

Answer 21

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

Answer 22

ya haha thats how i found it.

Answer 23

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

Answer 24

no sure go ahead

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

yeah thats what im checking up on lol

Answer 29

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

Answer 30

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

Answer 31

nope

Answer 32

im telling you ym prof was useless.

Answer 33

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

Answer 34

thanks man, i really appreciate it

Answer 35

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

Answer 36

how do you intergrate e^3t

Answer 37

its e^3t/3

Answer 38

everytime?, because won't the exponent increment?

Answer 39

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

Answer 40

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

Answer 41

Im glad to help really good luck!