Question

Calculate d/dx the equation is y=3x-9/2x+8

Answer 1

Ok alecv write the derivitives of f(x) and g(x)

Answer 2

ok f'(x) is 3 and g'(x) is 2

Answer 3

Ok now remember the quotient rule:

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

Plug in your equations

Answer 4

ok so I got 6/(2x+8)(2x+8)

Answer 5

ok im checking your work

Answer 6

I believe you forgot to distribute the minus sign again on the top:

\[\frac{ 6x+24 - (6x-18) }{ (2x+8)^2 }\]

Answer 7

hmm I tried that as well I believe it gives 42 it doesnt seem to like that either

Answer 8

Matt is right and 42 is the numerator.

Answer 9

so it should be 42/(2x+8)(2x+8)

Answer 10

Maybe it wants you to simplify though.

Answer 11

Do you know how to simplify?

Answer 12

could you refresh my memory? haha x)

Answer 13

2x+8 can be factored correct?

Answer 14

yes

Answer 15

Well 42 and (2x+8) share a common factor

Answer 16

The fraction can therefore be reduced.

Answer 17

the common factor is 2 so it turns the numerator into 21

Answer 18

does that then mean that the bottom becomes (x+4)?

Answer 19

Well you have
2x+8=2(x+4)
And you have (2x+8)^2 on bottom so that means you have 2(x+4)*2(x+4)

Only one of those 2's get canceled with a 2 from the top so yeah you can say the numerator is 21 now
but that would make the denominator what?

Answer 20

ok so you got 42 over 2(x+4)*2(x+4) like you said one of the 2's has cancels out with the 42 making 21 so that leaves you with (x+4) times 2(x+4) right?

Answer 21

cancelled*

Answer 22

Yep
Or 21/[2(x+4)^2]

Answer 23

Thank you soo much! I appreciate the help! i'm sure i'll be asking for your help again at some point today my professor gave us a boat load of homework

Answer 24

ok so again this time its asking for d/dx y=(x+6)(x^2-6) the x^2 is throwing me off