anonymous
  • anonymous
Take the derivative of: \[f(x)= \frac{ 5(2-x) }{ 3x^{1/3} }\]
Mathematics
chestercat
  • chestercat
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Loser66
  • Loser66
Where are you stuck?
Z4K4R1Y4
  • Z4K4R1Y4
use the quotient rule
anonymous
  • anonymous
I tried using the quotient rule, I kept on getting the wrong answer. :(

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Loser66
  • Loser66
show work, please
anonymous
  • anonymous
\[f'(x)=\frac{ -5(3x^{1/3}-10-5x(-x^{-4/3}) }{ 9x^{2/3} }\] I'm sure if this part is correct or not
anonymous
  • anonymous
There is suppose to be a bracket between the exponent 1/3 and subtraction sign
Loser66
  • Loser66
You MUST expand the parentheses before applying quotient rule OR let 5/3 in the front aside and take derivative the leftover by applying quotient rule. |dw:1433037281796:dw|
Loser66
  • Loser66
Or |dw:1433037313347:dw|
Loser66
  • Loser66
One more way: \(f(x) = \dfrac{10}{3}x^{-1/3} - \dfrac{5}{3}x^{2/3}\) , this form is the easiest one.
Loser66
  • Loser66
got the last one?
Loser66
  • Loser66
ok, \(\dfrac{1}{x} = x^{-1}\) right?
anonymous
  • anonymous
Whooh! There's so many ways to this question.
anonymous
  • anonymous
and yes, for 1/x
Loser66
  • Loser66
\(f(x) = \dfrac{10-5x}{3x^{1/3}}\) ok?
anonymous
  • anonymous
yes
Loser66
  • Loser66
|dw:1433037860682:dw|
Loser66
  • Loser66
|dw:1433037896740:dw|
anonymous
  • anonymous
I got here: \[\frac{ -10 }{ 9 }^{-4/3}-\frac{ 10 }{ 9 }x^{-1/3}\]
anonymous
  • anonymous
oops for I forgot the x. Is suppose to say x^(-4/3)
Loser66
  • Loser66
yup, correct
anonymous
  • anonymous
I'm not sure how to simplfy it more @Loser66
Loser66
  • Loser66
just bring them down to the denominator |dw:1433038167229:dw|
Loser66
  • Loser66
+ in parentheses ( typo)
Loser66
  • Loser66
To me, just let it as it is, you will have the full credit. No need to simplify.
Loser66
  • Loser66
Because if you do more, it turns complicated since \(x^{4/3}=\sqrt[3] x^4\) ugly!!
anonymous
  • anonymous
Just wondering if this is right? \[\frac{ 10(x+1) }{ 9^{4/3} }\]
Loser66
  • Loser66
No
Loser66
  • Loser66
I meant - infront.
Loser66
  • Loser66
then you are right.
anonymous
  • anonymous
oh oops! Thank you!

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