Question

Find the derivative of the function.

y = (x^2-4)^(1/2) - 2 arcsec(x/2)

Answer 1

so, any initial thoughts?

Answer 2

Well, I was able to find the derivative of arcsec(x/2) -- without simplifying.

Answer 3

@FibonacciChick666 -- this what I got for that part.

Answer 4

ok, and what did you get?

Answer 5

\[\frac{ d }{ dx }[arsec \frac{ x }{ 2 }] = \frac{ \frac{ 1 }{ 2 } }{ |\frac{ x }{ 2 }|\sqrt{(\frac{ x }{ 2 })^2-1}}\]

Answer 6

*arcsec

Answer 7

ok i can buy that, now how about the first part?

Answer 8

I know it's the chain rule (it still confuses me a bit), but I would have to re-write it.

\[y = (x^2-4)^{1/2}\]

Answer 9

\[y \prime = \frac{ 1 }{ 2 } * (x^2-4)^{-1/2} * 2x\] I think maybe? :/ Am I right @FibonacciChick666

Answer 10

yup yup

Answer 11

it's that simple

Answer 12

now, you can take a longer approach to make it easier on your brain though
if you say let \[u=x^2-4\]\[du=2x\]
so now you have \[y=u^\frac{1}{2}\]

Answer 13

if that helps

Answer 14

Hah, yeah. It's trying to get that final answer. So many algebraic things that are easy to mess up.

Answer 15

true true

Answer 16

but you have it, just be confident

Answer 17

if you're worrid about messing up, always do the substitution on the side

Answer 18

Yeah, that's what I've been doing. It's tedious and time-consuming, but I've found it helps.

Answer 19

it does, and it will help when you get to integration by parts to be in the habit

Answer 20

you'll get better with practice :)

Answer 21

medal?