- anonymous

find the derivative of f(x) = (3x^2 - 3x + 1)/(2x). Directions, put 2x under each term and simplify. Then take the derivative.

- jamiebookeater

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- anonymous

@satellite73 can u help?

- anonymous

@onegirl hints has been given in the ques
so what will u get after simplifying ?

- anonymous

ok hold on

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## More answers

- anonymous

after i put 2x over each term
f(x) = 3x^2/2x â 3x/2x + 1/2x
f(x) 3/2 x + 3/2 + 1/2x
fâ(x) = 3/2 + 0 - 1/2x^2
fâ(x) = 3x^2 â 1

- anonymous

last step is wrong
u forgot to write in denominator?

- anonymous

what step?

- anonymous

for f'(x) = 3x^2 - 1?

- anonymous

yeah

- anonymous

ohh

- anonymous

so 3x^2 -1/2x?

- Mertsj

\[f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x ^{-1}\]

- anonymous

it will be 3x^2-1/2x^2

- anonymous

okay

- anonymous

so what do i do after that?

- anonymous

it is ur answer

- Mertsj

\[f'(x)=\frac{3}{3}-\frac{1}{2}x ^{-2}\]

- anonymous

so thats my derivative?

- Mertsj

Whoops. Typo. Should be 3/2 not 3/3

- anonymous

yeah thats your derivative

- anonymous

okay ii guess not putting 2x^2 is why i got it wrong

- anonymous

yeah

- anonymous

thx

- Mertsj

You were supposed to put 2x UNDER each term

- anonymous

yea i did

- anonymous

@Mertsj so i did it wrong?

- anonymous

@zepdrix can u help please? did i do it right or wrong?

- zepdrix

|dw:1362685192013:dw|Do you understand this step? ~Splitting up the fractions.
I wrote those ugly blobs to help show how we'll split it up.

- anonymous

ok

- anonymous

i see now

- anonymous

yea i understand that step

- zepdrix

So the x's will divide in the middle term.
Do you understand how to simplify the first term?

- anonymous

let me try

- anonymous

i got (3x^2 - 3x + 1)/(2x)

- Mertsj

Yep. Now split it up into 3 fractions like your teacher said.

- zepdrix

ya you took a step backwards.. that was strange :c

- anonymous

okay so i put 2x under each of those 3 fractions?

- anonymous

i did?

- Mertsj

Put 2x UNDER each term. The first term is 3x^2

- zepdrix

You didn't "get" (3x^2 - 3x + 1)/(2x).
You STARTED with that :)
The first step was to split it into 3 fractions.

- anonymous

ok so 3x^2/2x - 3x/2x + 1/2x

- anonymous

Ohhh okay got u

- Mertsj

There you go.

- zepdrix

yes, now simplify each fraction c: Don't combine them back together though! heh

- anonymous

ok

- anonymous

hold on lol sorry

- anonymous

ok so i got 3x/2 - 3/2 + 1/2x after simplifying

- zepdrix

k looks good c:
Let's rewrite it in a way that will be easier to take a derivative of.

- anonymous

ok

- zepdrix

\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{1}{2x}}\]In the last term, we can bring the x up to the numerator by applying a negative exponent to it.\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{x^{-1}}{2}}\]

- zepdrix

Let's pull those X's off of the fraction bar, it will be easier to read if we just have coefficients in front of our X's.
\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\frac{1\cdot x^{-1}}{2} \qquad \rightarrow \qquad f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x^{-1}\]

- anonymous

okay

- anonymous

so now i can just find the derivative of 3/2 x - 3/2 + 1/2 x ^-1

- zepdrix

yah sounds good.

- anonymous

okay i'll find the derivative thx!

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