anonymous
  • anonymous
I need help in calculus. Can anyone?
Calculus1
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anonymous
  • anonymous
I need help in calculus. Can anyone?
Calculus1
katieb
  • katieb
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amistre64
  • amistre64
calculus 1? hmm
amistre64
  • amistre64
posting the question might be prudent
anonymous
  • 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?

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amistre64
  • amistre64
using derivative rules or the other way?
amistre64
  • amistre64
is that cot^5 a top or bottom of the fraction?
anonymous
  • anonymous
Using the rules. It's on top.
amistre64
  • amistre64
are those x/3 arguements of the trig function, or is that trig divided by 3?
amistre64
  • amistre64
\[y=-\frac35\cot^5 (\frac{x}3)+\cot^3 (\frac{x}3)-3\cot (\frac{x}3) -x\]
anonymous
  • anonymous
Yes that's it!
amistre64
  • 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?
amistre64
  • amistre64
what is your power rule?
anonymous
  • anonymous
nu^n-1 du/dx
amistre64
  • amistre64
good, lets use u' instead of du/dx just simpler to write
amistre64
  • 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)?
amistre64
  • amistre64
bah, code typo .... -3u^4
amistre64
  • amistre64
u' is a chain rule as well ... what is your chain rule?
anonymous
  • anonymous
nu^n-1 du/dx
amistre64
  • amistre64
no, thats power rule .... chain rule is for composition of function
amistre64
  • 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'
anonymous
  • anonymous
3/5cot^5(x/3) will be like this 3/5 (5)cot^4(-x/9)(-csc^2x)?
amistre64
  • 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)
anonymous
  • anonymous
Really going to be a tough one for me.
amistre64
  • 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 \[y'=\csc^2(\frac{x}3)~(\cot^4(\frac{x}3) -\cot^2(\frac{x}3) +\frac13) ~-1\]
amistre64
  • amistre64
its not a difficult process, just messy if you try to keep it all ... x-ish thru the process
anonymous
  • anonymous
I'll try for it. This is, one part of Differential Calculus that I'm really having a hard time.
amistre64
  • amistre64
it can be daunting, but its really simpler than algebra :) good luck
anonymous
  • anonymous
Maybe but I don't really know. Thanks.

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