anonymous one year ago Take the derivative of: $f(x)= \frac{ 5(2-x) }{ 3x^{1/3} }$

1. Loser66

Where are you stuck?

2. Z4K4R1Y4

use the quotient rule

3. anonymous

I tried using the quotient rule, I kept on getting the wrong answer. :(

4. Loser66

5. 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

6. anonymous

There is suppose to be a bracket between the exponent 1/3 and subtraction sign

7. 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|

8. Loser66

Or |dw:1433037313347:dw|

9. Loser66

One more way: $$f(x) = \dfrac{10}{3}x^{-1/3} - \dfrac{5}{3}x^{2/3}$$ , this form is the easiest one.

10. Loser66

got the last one?

11. Loser66

ok, $$\dfrac{1}{x} = x^{-1}$$ right?

12. anonymous

Whooh! There's so many ways to this question.

13. anonymous

and yes, for 1/x

14. Loser66

$$f(x) = \dfrac{10-5x}{3x^{1/3}}$$ ok?

15. anonymous

yes

16. Loser66

|dw:1433037860682:dw|

17. Loser66

|dw:1433037896740:dw|

18. anonymous

I got here: $\frac{ -10 }{ 9 }^{-4/3}-\frac{ 10 }{ 9 }x^{-1/3}$

19. anonymous

oops for I forgot the x. Is suppose to say x^(-4/3)

20. Loser66

yup, correct

21. anonymous

I'm not sure how to simplfy it more @Loser66

22. Loser66

just bring them down to the denominator |dw:1433038167229:dw|

23. Loser66

+ in parentheses ( typo)

24. Loser66

To me, just let it as it is, you will have the full credit. No need to simplify.

25. Loser66

Because if you do more, it turns complicated since $$x^{4/3}=\sqrt[3] x^4$$ ugly!!

26. anonymous

Just wondering if this is right? $\frac{ 10(x+1) }{ 9^{4/3} }$

27. Loser66

No

28. Loser66

I meant - infront.

29. Loser66

then you are right.

30. anonymous

oh oops! Thank you!