## anonymous one year ago I need help in calculus. Can anyone?

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1. amistre64

calculus 1? hmm

2. amistre64

posting the question might be prudent

3. anonymous

Sorry for a late reply. Can you help me find the derivative of this y=-3/5cot^5 x/3+cot^3 x/3-3cot x/3 -x?

4. amistre64

using derivative rules or the other way?

5. amistre64

is that cot^5 a top or bottom of the fraction?

6. anonymous

Using the rules. It's on top.

7. amistre64

are those x/3 arguements of the trig function, or is that trig divided by 3?

8. amistre64

$y=-\frac35\cot^5 (\frac{x}3)+\cot^3 (\frac{x}3)-3\cot (\frac{x}3) -x$

9. anonymous

Yes that's it!

10. amistre64

if we let u=cot(x/3) $y=-\frac35u^5 +u^3 -3u -x$ how would you attempt to find the derivative of this?

11. amistre64

12. anonymous

nu^n-1 du/dx

13. amistre64

good, lets use u' instead of du/dx just simpler to write

14. amistre64

$y=-\frac35u^5 +u^3 -3u -x$ $y'=-\frac3u^4u' +3u^2u' -u' -x'$ x'=dx/dx=1 soo $y'=u'(-\frac3u^4 +3u^2 -1) -1$ oh, and what will our u' be since u=cot(x/3)?

15. amistre64

bah, code typo .... -3u^4

16. amistre64

u' is a chain rule as well ... what is your chain rule?

17. anonymous

nu^n-1 du/dx

18. amistre64

no, thats power rule .... chain rule is for composition of function

19. amistre64

a function within a function, within a function, within a function .... f(g(h(...(k(x))))) the derivative is a multiplier effect: f'g'h'...k'

20. anonymous

3/5cot^5(x/3) will be like this 3/5 (5)cot^4(-x/9)(-csc^2x)?

21. amistre64

close, but i like to work with a simpler writeup 3/5 u^5 would be 3u^4 u' but since u = cot(x/3), u' = -csc^2(x/3) * (x/3)'; or -1/3 csc^2(x/3)

22. anonymous

Really going to be a tough one for me.

23. amistre64

let u = cot(x/3); u' = -1/3 csc^2(x/3) $y'=u'(-3u^4 +3u^2 -1) -1$ $y'=-\frac13\csc^2(\frac{x}3)~(-3\cot^4(\frac{x}3) +3\cot^2(\frac{x}3) -1) -1$ or $y'=\csc^2(\frac{x}3)~(\cot^4(\frac{x}3) -\cot^2(\frac{x}3) +\frac13) ~-1$

24. amistre64

its not a difficult process, just messy if you try to keep it all ... x-ish thru the process

25. anonymous

I'll try for it. This is, one part of Differential Calculus that I'm really having a hard time.

26. amistre64

it can be daunting, but its really simpler than algebra :) good luck

27. anonymous

Maybe but I don't really know. Thanks.