Question

WILL GIVE MEDALS! can anyone help me figure out how they got the simplified answer? i feel like they jumped alot of steps or something. the picture is posted below

Answer 1

where?

Answer 2

@blm1

Answer 3

i knew how to take the derivative, but the simplifying is messing me up :(

Answer 4

@phi

Answer 5

@welshfella

Answer 6

Do you understand the line following the line that says Apply the quotient rule?

Answer 7

yes

Answer 8

Do you also understand the derivative of x is 1, and the next derivative?

Answer 9

yes, i was able to take the derivative in its entirety, i just don't understand how they went from -48 times (....) to the simplified 144 times (...)

Answer 10

how did they simplify all that?

Answer 11

Ok. Let's go through it step by step.

Answer 12

please! thatd be awesome

Answer 13

\(-48\dfrac{1(x^2 + 12)^2 - 4x(x^2 + 12)x}{((x^2 + 12)^2)^2} \)

Answer 14

Distribute the -48 and raise the denominator to the 2nd power.

\(=\dfrac{-48(x^2 + 12)^2 +192x(x^2 + 12)x}{(x^2 + 12)^4} \)

Answer 15

okay

Answer 16

Both terms in the numerator and the denominator have a common factor of \(x^2 + 12\), so divide all terms by \(x^2 + 12\).

\(=\dfrac{-48(x^2 + 12) +192x^2}{(x^2 + 12)^3} \)

Answer 17

ohhh okay

Answer 18

Distribute the -48 in the numerator and combine like terms.

\(=\dfrac{-48x^2 -576 +192x^2}{(x^2 + 12)^3} \)

\(=\dfrac{144x^2 -576}{(x^2 + 12)^3} \)

Factor out 144.

\(=\dfrac{144(x^2 -4)}{(x^2 + 12)^3} \)

Answer 19

Just a little algebra manipulation.

Answer 20

oh wow thank you so much

Answer 21

You're welcome.