Question

Given that d/dx 1-2x / square root (2+x^2) = g(x)/ square root (2+x^2)^3 ,find g(x).

Answer 1

Let's just clear a few ambiguities...
<ahem>

Given that \[\Large \frac{d}{dx}\left[\frac{1-2x}{\sqrt{2+x^2}}\right]=\frac{g(x)}{(2+x^2)^3}\]

find \(\large g(x)\)

Is that it? :)

Answer 2

correct

Answer 3

but must square root at the deneminator for RHS

Answer 4

Well, the typical way I'd go about this is drop everything and just find the derivative of
\[\Large \frac{1-2x}{\sqrt{2+x^2}}\]
outright :D

At least, first...

Answer 5

my final answer for numerator is x + 4 i'm not sure whether there is a x

Answer 6

Wait what?
More like this?
\[\Large \frac{g(x)}{\left[\sqrt{2+x^3}\right]^3}\]

Answer 7

The cube belongs to the (2 + x^2) ^3/2

Answer 8

Okay, much more acceptable :3
\[\Large \frac{g(x)}{(2+x^2)^{\frac32}}\]
This, then?

Answer 9

yes

Answer 10

okay, well, let's go about differentiating
\[\Large \frac{1-2x}{\sqrt{2+x^2}}\]
Or have you already done that?

Answer 11

i did that and my numerator i got x +4 is that right?

Answer 12

I took out the negative sign in my numerator.

Answer 13

Hang on...

Answer 14

Oh. Well, you're asked what g(x) is, meaning the entire numerator, so you have to include the negative ...
so it should be -x - 4