Question

I need help in calculus. Can anyone?

Answer 1

calculus 1? hmm

Answer 2

posting the question might be prudent

Answer 3

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?

Answer 4

using derivative rules or the other way?

Answer 5

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

Answer 6

Using the rules. It's on top.

Answer 7

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

Answer 8

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

Answer 9

Yes that's it!

Answer 10

if we let u=cot(x/3)

\[y=-\frac35u^5 +u^3 -3u -x\]
how would you attempt to find the derivative of this?

Answer 11

what is your power rule?

Answer 12

nu^n-1 du/dx

Answer 13

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

Answer 14

\[y=-\frac35u^5 +u^3 -3u -x\]
\[y'=-\frac3u^4u' +3u^2u' -u' -x'\]
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)?

Answer 15

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

Answer 16

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

Answer 17

nu^n-1 du/dx

Answer 18

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

Answer 19

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'

Answer 20

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

Answer 21

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)

Answer 22

Really going to be a tough one for me.

Answer 23

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
\[y'=\csc^2(\frac{x}3)~(\cot^4(\frac{x}3) -\cot^2(\frac{x}3) +\frac13) ~-1\]

Answer 24

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

Answer 25

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

Answer 26

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

good luck

Answer 27

Maybe but I don't really know. Thanks.