Question

what is the derivative of f(x) 2x / x + 2

Answer 1

I know its f'g - fg' / g^2

Answer 2

but that is the derivative of x+ 2

Answer 3

\(\large\color{black}{f(x)= \frac{\LARGE 2x }{\LARGE x+2} }\) like this?

Answer 4

yeah

Answer 5

then I would re-write it as: \(\large\color{black}{f(x)= (2x)(x+2)^{-1} }\) and use the product rule.

Answer 6

I have to use the quotient rule because that is what the direction says

Answer 7

And I like quotient rule more I understand it better

Answer 8

so far I have 2(x+2) - 2x

Answer 9

then for \(f(x) = \frac{g(x)}{h(x)}\) we have \(f'(x)=\frac{g'(x)h(x)-g(x)h'(x)}{h(x)^2}\)

Answer 10

the quotient rule is: \(\large\color{black}{ \frac{\LARGE g(x)f'(x)-f(x)g'(x)}{\LARGE g(x)} }\)

Answer 11

but that over (x+2)^2

Answer 12

put that over*

Answer 13

what is the derivative of x + 2 ?

Answer 14

1

Answer 15

you are almost done, you forgot the easy part

\(\frac{2(x+2)-2x}{(x+2)^2}=\frac{2x+4-2x}{(x+2)^2}=\frac{4}{(x+2)^2}\)

Answer 16

how do I simplify 2- 2x / x+ 2

Answer 17

\(\huge \uparrow\)

Answer 18

wait I did not do it that way :(

Answer 19

I got to the second part but instead of getting 4 there is (x +2) on the top and bottom so I took it off

Answer 20

well I divided it and got 2- 2x / x+ 2