Question

trying to find the second derivative in this question......3x-3 over 2x+4. the Vertical Asy is -2 and the Horizontal Asy is 3/2...the xint is (1,0) and the yint is (0,-3/4) please give me step buy step

Answer 1

can you find the first derivative? because that is the only hard part

Answer 2

quotient rule give
\[\frac{d}{dx}\frac{3x-3}{2x+4}=\frac{(2x+4)\times 3-(3x+3)\times 2}{(2x+4)^2}\]

Answer 3

yes i have the first one all ready

Answer 4

so you end up with
\[\frac{9}{(2x+4)^2}=9(2x+4)^{-2}\] now second should be easy

Answer 5

\[-18(2x+4)^{-3}\times 2=-36(2x+4)^{-3}=-\frac{36}{(2x+4)^3}\]

Answer 6

you can cancel a little because
\[(2x+4)^3=(2(x+2))^3=8(x+2)^3\]

Answer 7

im so confused

Answer 8

ok which step? did you get the first derivative?

Answer 9

i got (2x+4)-2(3x-3) over (2x+4)^2

Answer 10

then you have to do the algebra in the numerator

Answer 11

should be
\[(2x+4)3-2(3x-3) \]

Answer 12

in front of the 2x+4 there is suppose to be a 3

Answer 13

yes it is the denominator times the derivative of the numerator as the first term

Answer 14

minus the numerator times the derivative of the denominator

Answer 15

if you multiply out the x terms add up to zero and you get 9

Answer 16

so 18 over (2x+4)^2 ?

Answer 17

yes

Answer 18

\[(2x+4)3-2(3x-3)\]
\[6x+12-6x+6=18\] yes

Answer 19

my equation is 3(2x+4)-2(3x-3)

Answer 20

yes multiply out and you will get 18

Answer 21

ok then what do i do to get the second answer

Answer 22

you have
\[\frac{18}{(2x+4)^2}\] so rather than using the quotient rule again, rewrite in exponential form as
\[18\times (2x+4)^{-2}\] and use the power rule (and the chain rule)

Answer 23

ok so multiple it out?

Answer 24

power rule right?
\[\frac{d}{dx}x^n=nx^{n-1}\]

Answer 25

i made a mistake, sorry

Answer 26

\[\frac{d}{dx}18(2x+4)^{-2}=-2\times 18(2x+4)^{-2-1}\times 2\]
\[=-72(2x+4)^{-3}=-\frac{72}{(2x+4)^3}\] but you can simplify this

Answer 27

because
\[(2x+4)^3=(2(x+2))^3=8(x+2)^3\] and \[\frac{72}{8}=9\]

Answer 28

so your "final answer" will be
\[-\frac{9}{(x+2)^3}\]

Answer 29

thank you so much

Answer 30

yw