Question

derivative of (x^2-4)/(x)
I have 2x^2-x^2+4 so far...

Answer 1

ohh divided by x^2

Answer 2

Ohh yes :3 good catch hehe

Answer 3

yes! lol but can it be reduced?:O

Answer 4

One sec, I wanna check your work ^^\[\Large \left[\frac{x^2-4}{x}\right]'\quad=\quad \frac{\color{royalblue}{(x^2-4)'}(x)-(x^2-4)\color{royalblue}{(x)'}}{x^2}\]

Answer 5

\[\Large =\frac{\color{royalblue}{(2x)}(x)-(x^2-4)\color{royalblue}{(1)}}{x^2}\]

Answer 6

Mmm ok ok ok looks like you're on the right track.
reduced? Hmm

Answer 7

yay:) & yes because can't you simplify after you foil??

Answer 8

No, after combining the terms in the numerator, you should probably leave it alone :)
\[\Large \frac{x^2+4}{x^2}\]

Hmm there is no foil :D See how the (x^2-4) is just being multiplied by 1? +_+

Answer 9

Oh so you don't multiply the 2x and the x to get 2x^2?? :O

Answer 10

You do ^^ sorry I skipped that step D:

Answer 11

that's how I got (2x^2-x^2+4)/x^2
and then I assume you can reduce & get 2-1+4 = 5?? or am I wrong?

Answer 12

You can combine the `x^2`s since they're like terms.
\[\Large 2x^2-x^2 \quad=\quad x^2\]

Answer 13

I'm not sure what you're doing with the 4 there though 0_o hmm

Answer 14

Oh oh oh i see, you were trying to divide x^2 out?

Answer 15

You forgot to divide x^2 from the last value, 4.

It would leave you with 4/x^2, not just 4.

Answer 16

That's why we want to leave it alone :O no division.

Answer 17

yes but idk if that's right:o

Answer 18

but wait doesn't the x^2 get cancelled out when it's reduced??

Answer 19

\[\Large \frac{2x^2-x^2+4}{x^2} \quad\color{red}{\ne}\quad 2-1+4\]
\[\Large \frac{2x^2-x^2+4}{x^2} \quad=\quad 2-1+\frac{4}{x^2}\]

Answer 20

ohh :0 so it would be 1+4/x^2

Answer 21

that's so true I forgot to divide that last part!

Answer 22

Yes, you could write it like that if you want :)
Or you can leave the x^2s on top which looks a little nicer.

\(\Large \dfrac{x^2+4}{x^2}\qquad\)or\(\Large \qquad1+\dfrac{4}{x^2}\)

Either way is fine ^^

Answer 23

Got it :) thanks @zepdrix !!! :D

Answer 24

yay team \c:/

Answer 25

^.^