anonymous
  • anonymous
find the derivative of f(x) = (3x^2 - 3x + 1)/(2x). Directions, put 2x under each term and simplify. Then take the derivative.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@satellite73 can u help?
anonymous
  • anonymous
@onegirl hints has been given in the ques so what will u get after simplifying ?
anonymous
  • anonymous
ok hold on

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

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