onegirl
find the derivative of f(x) = (3x^2 - 3x + 1)/(2x). Directions, put 2x under each term and simplify. Then take the derivative.
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onegirl
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@satellite73 can u help?
niksva
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@onegirl hints has been given in the ques
so what will u get after simplifying ?
onegirl
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ok hold on
onegirl
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after i put 2x over each term
f(x) = 3x^2/2x – 3x/2x + 1/2x
f(x) 3/2 x + 3/2 + 1/2x
f’(x) = 3/2 + 0 - 1/2x^2
f’(x) = 3x^2 – 1
niksva
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last step is wrong
u forgot to write in denominator?
onegirl
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what step?
onegirl
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for f'(x) = 3x^2 - 1?
niksva
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yeah
onegirl
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ohh
onegirl
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so 3x^2 -1/2x?
Mertsj
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\[f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x ^{-1}\]
niksva
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it will be 3x^2-1/2x^2
onegirl
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okay
onegirl
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so what do i do after that?
niksva
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it is ur answer
Mertsj
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\[f'(x)=\frac{3}{3}-\frac{1}{2}x ^{-2}\]
onegirl
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so thats my derivative?
Mertsj
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Whoops. Typo. Should be 3/2 not 3/3
niksva
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yeah thats your derivative
onegirl
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okay ii guess not putting 2x^2 is why i got it wrong
niksva
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yeah
onegirl
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thx
Mertsj
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You were supposed to put 2x UNDER each term
onegirl
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yea i did
onegirl
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@Mertsj so i did it wrong?
onegirl
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@zepdrix can u help please? did i do it right or wrong?
zepdrix
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|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.
onegirl
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ok
onegirl
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i see now
onegirl
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yea i understand that step
zepdrix
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So the x's will divide in the middle term.
Do you understand how to simplify the first term?
onegirl
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let me try
onegirl
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i got (3x^2 - 3x + 1)/(2x)
Mertsj
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Yep. Now split it up into 3 fractions like your teacher said.
zepdrix
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ya you took a step backwards.. that was strange :c
onegirl
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okay so i put 2x under each of those 3 fractions?
onegirl
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i did?
Mertsj
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Put 2x UNDER each term. The first term is 3x^2
zepdrix
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You didn't "get" (3x^2 - 3x + 1)/(2x).
You STARTED with that :)
The first step was to split it into 3 fractions.
onegirl
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ok so 3x^2/2x - 3x/2x + 1/2x
onegirl
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Ohhh okay got u
Mertsj
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There you go.
zepdrix
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yes, now simplify each fraction c: Don't combine them back together though! heh
onegirl
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ok
onegirl
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hold on lol sorry
onegirl
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ok so i got 3x/2 - 3/2 + 1/2x after simplifying
zepdrix
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k looks good c:
Let's rewrite it in a way that will be easier to take a derivative of.
onegirl
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ok
zepdrix
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\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\color{orangered}{\frac{1}{2x}}\]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
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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.
\[\large f(x)=\frac{3x}{2}-\frac{3}{2}+\frac{1\cdot x^{-1}}{2} \qquad \rightarrow \qquad f(x)=\frac{3}{2}x-\frac{3}{2}+\frac{1}{2}x^{-1}\]
onegirl
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okay
onegirl
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so now i can just find the derivative of 3/2 x - 3/2 + 1/2 x ^-1
zepdrix
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yah sounds good.
onegirl
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okay i'll find the derivative thx!