Question

find dy/dx

Answer 1

\[y = 2x/\sqrt{x+8}\]

Answer 2

hi i got stuck

Answer 3

USE THE QUOTIENT RULE!!!!!

Answer 4

Heya. Quotient rule :P So let's follow our formula.

\[\frac{ f'(x)g(x) - f(x)g'(x) }{ [g(x)]^{2} }\]

Answer 5

i know i know

Answer 6

but i got stuck in a part im asking what to do next

Answer 7

here this is where i got stuck

Answer 8

\[f(x) = 2x\]
\[g(x) = \sqrt{x+8}\]
\[f'(x) = 2\]

So the f'(x) was obvious. what do you get for g'(x)? We can get ya worked along from there :3

Answer 9

dy/dx = 2(x+8)^1/2 - (x)(x+8)^-1/2 all divide by x+8

Answer 10

this is where im lost at

Answer 11

just plug in the numbers dude

Answer 12

do u go to k12?

Answer 13

(2)(x+8)^1/2 - 1/2 (x+8)^-1/2(2x) / x+8

Answer 14

Noooooo

Answer 15

no?

Answer 16

let me explain

Answer 17

Alright, so ill type it out and see how it looks compared to mine as we go.

\[\frac{ 2\sqrt{x+8} - \frac{ 2x(x+8)^{-1/2} }{ 2 } }{ x+8 }\]

\[\frac{ 2(x+8)^{1/2} - x(x+8)^{-1/2} }{ x+8 }\]
Okay, so theres a few ways we can do this next step. We can start stacking fractions, moving the -1/2 power down or we can do some factoring out.

Answer 18

wtf thats what i got

Answer 19

If I factor out, I want to factor out a (x+8)^(-1/2). When you factor out negative powers, instead of taking away from all the exponents by the amount factored, you ADD by the amount factored. So factoring out a -1/2 exponent will add 1/2 to the other exponents for that same group. So it'll end up like this:

Answer 20

\[\frac{ (x+8)^{-1/2}[2(x+8)-x] }{ x+8 }\]

Answer 21

ooooooo ok

Answer 22

then u simplify like redistrubte the 2

Answer 23

gets u x+16 on the inside

Answer 24

You just have to be careful with how you factor, especially since its a large termwith a negative exponent. From here, I am safe to move the (x+8)^(-1/2) term down and simplify inside of the brackets:

\[\frac{ x+16 }{ (x+8)^{1/2}(x+8) }= \frac{ x+16 }{ (x+8)^{3/2} }\]

Answer 25

(x+8)^-1/2 ( x+16) / x+8

Answer 26

okay thanks concentrationalizing again :D!!!

Answer 27

Yep np :3 Are you okay with that kind of factoring?

Answer 28

kind of lol thats why im praticing more

Answer 29

i didnt know what was the next step i forgot u had to factor

Answer 30

Gotcha. I think its safer than the stacking fractions way. You can move the negative expoennt term down, but it forces you to have 3 levels of fractions.

Answer 31

yeah no doubt thnx !! i will repost when im stuck again with something!! ty so much

Answer 32

Np : )