Question

lets see... (another fund. trm of calc Q.)

Answer 1

the final answer is right
i just don't like the work before it

Answer 2

\[\text{ i would rewrite what you said like this } \\ (\tan(x))'f(\tan(x))= \sqrt{...} \cdot \frac{d}{dx}\tan(x)\]
I didn't feel like writing all that stuff in the square root :p

Answer 3

not a big deal

Answer 4

it was just not exactly equal :p

Answer 5

wait, so you are saying the same thing, aren't you? except that you are saying
(tan x)' * F'(tan x)
and I wrote the whole f(tan x) out and multiplied times the derivative of tan(x)

Answer 6

substituted tan(x) instead of "t", (removing the integral as given by fund. trm, which makes sense) and used a chain rule , i.e. times (tan x)'

Answer 7

I know everything you did is right
I just don't like that equality because they weren't exactly equal
f(x)=sqrt(x+sqrt(x))
f(tan(x)=sqrt(tan(x)+sqrt(tan(x))

Answer 8

oh, I thought you are saying i was wrong.

Answer 9

I see...

Answer 10

i didn't say you were wrong
i just said i didn't like the work above

Answer 11

only because the equality wasn't exactly true

Answer 12

the only reason i said something about it is because a teacher would too

Answer 13

or some teachers would

Answer 14

well, it is normal to understand "didn't like" this way, also i think I didn't leave out the chain rule for the deriv. of tan x

Answer 15

ok well i don't care if you don't care

Answer 16

So, as far as the work goes, I don't see any errors.

I said,

f(tan x) = ....

Answer 17

i am thinking that I got the idea here... still don't see any even smallest errors in what I wrote, but I will go over when I have time.
(I am really busy doing h/w sorry)

Answer 18

\[y=\int\limits^{\tan x}_{0} \sqrt{t+ \sqrt{t}}~~dt\]

are you defining \(f(t) = \sqrt{t+\sqrt{t}}\) ?

Answer 19

yes, if my head isn't broken.

Answer 20

then isn't \(f(\tan x) = \sqrt{\tan x + \sqrt{\tan x}}\) ?

Answer 21

the chain rule for the tanx ?

Answer 22

why do you need chain rule, you aren't differentiating anything yet
you have just definited a function and taking composition with another function \(g(x) = \tan x\) right ?

Answer 23

suppose you're in algebra2, how would you answer to below question ?
\[f(t) = \sqrt{t+\sqrt{t}}\]
\[f(\tan x) = ?~~~~~~~~~~~~~~~~~~~~~~~\]

Answer 24

I am not sure about the definition, I tricked myself and ya'll I guess.

What I was saying that (with any C)