Question

Calculate the derivatives of the following real functions by using the chain rule; maybe several times. In each case, determine the inner and outer function to be used, together with their respective areas of definition.
d) \(h(x) = \sqrt{2+exp(x^{2})}\)

Answer 1

derivative of outside function, evaluated at the inside function, times the derivative of the inside function

Answer 2

hey @satellite73 thank you but i am not so good at math, pls help me more, in about 5 hours i need to give up homework :)
and i can write you a message unfortunately..its blocked i think.

Answer 3

*cant

Answer 4

I refuse to accept the label "not good at math"
especially when someone has made it to calculus

Answer 5

the derivative of the square root of something is one of two times root of something, times the derivative of something

Answer 6

more succinctly written as
\[\frac{d}{dx}\sqrt{f(x)}=\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 7

@TuringTest thank you, i didnt really understand what you mean but i think you are saying something good (my english is bad as my math)

Answer 8

no worries, I'm just saying that you should not decide that you are bad at math so quickly

Answer 9

aah ok, i understood like that but i was not sure :) thanks, i need to be good at math very soon i have exam next month, and i had always problem wit this lecture in germany we are sayng its a analysis i think in america its calculus

Answer 10

so here your \(f(x)=2+\exp(x^2)\) and so your \(f'(x)=2x\exp(x^2)\)

Answer 11

math analysis=calculus in English too :)

Answer 12

and therefore you answer is
\[\frac{2x\exp(x^2)}{2\sqrt{2+\exp(x^2)}}\] make sure to cancel the 2 so your professor does not think you are daft

Answer 13

@satellite73 ok.. which 2 you mean?
@TuringTest but i think this time i can do it with exam becuase i found openstudy here so many people who like to help, but the problem is until this days i didnt had much time to learn,

Answer 14

\[\frac{\cancel{2}x\exp(x^2)}{\cancel{2}\sqrt{2+\exp(x^2)}}\]

Answer 15

aah ok thanks Zarkon

Answer 16

Please keep coming to Open Study for help, that is our goal
@satellite73 and @Zarkon are some of the best, so they can sure help you :)

Answer 17

i love \(\cancel{cancel}\)

Answer 18

I'm lazy and don't help much

Satellite is good though ;)

Answer 19

@satellite73 thank you very much
@TuringTest yes i know, Sattelite helping me much, Zarkon he helped first today but its ok :) sorry if i forget that you helped maybe

Answer 20

Zarkon only provides the most minimal detail possible, which I love because it forces you to think.
Satellite is more explanatory; just a different style I guess

Answer 21

yes Zarkons help i will need before exam, when i learned and need details :)

Answer 22

as you said

Answer 23

I use the moore method...you do more and I do less ;)

Answer 24

:D

Answer 25

@Zarkon you have "giant footsteps" though, as asnaseer says. One hint from Zarkon is worth twenty from me.... in my opinion at least

Answer 26

TT you are an excellent tutor...more often more helpful than I am.

Answer 27

@TuringTest are you computer scientist or mathematician?

Answer 28

praise from Caesar :D

Answer 29

I am a lowly student

Answer 30

for those that don't know there is a Moore method...
http://en.wikipedia.org/wiki/Moore_method

Answer 31

ha, I thought you just made that up!

Answer 32

I took two classes where the Moore method was used...topology and geometry

Answer 33

geometry? some super special Reimannian Manifold geometry or something o-0

Answer 34

we built up euclidean geometry from the ground up. It was a senior level undergraduate class.

Answer 35

the prof just gave definitions and axioms...and the students had to prove all the theorems

Answer 36

no lecture

Answer 37

are you both in same university ?

Answer 38

cool :)
that's I had a similar experience in geometry in high school that led me to feel confident in math, but that story is for another time :)
and no @tunahan , Zarkon is a master, a real pro
I'm just a student

Answer 39

I am no longer a student.

Answer 40

...and we live in different countries, etc.
I just like to tutor

Answer 41

ok :) i thought the most of the people here is from usa

Answer 42

i thought even they are the most from same university..

Answer 43

we both are, but I live in mexico
but this site has a nice mix of US, European, middle-eastern and asian students

Answer 44

ok this site is really helpfull, if see who made it, i would like to thank him or people who has done..

Answer 45

Some math professors also stop by to help

Answer 46

@tunahan I'm glad you find value in the purpose of this site.
I hope you continue to come here, and become an integral part of OS
you could really contribute with that attitude!

Answer 47

yes this site is really like a treausre for me, OS is not Operating System right :) ?

Answer 48

Not in this case
OS=Open Study
(sorry, I just type it so many times a day...)

anyway, I've got to go

pleasure talking to you, see you around!

Answer 49

sorry i am stupid :) i would know that u mean Open Study, i am computer science student, and mad with operating systems, ok it was pleausre to talking with you Turing, i have more questions today, you can both take a look if you would like to

Answer 50

@Zarkon here is my question may be you would like to solve for me so that i get good points from my mentor :)
http://openstudy.com/study#/updates/4fe3d9aae4b06e92b8729084