anonymous
  • anonymous
Find dy/dx if y= tan(cos(e^sqrt(x^2+1)))
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
its just an application of chaining a chain ....
amistre64
  • amistre64
\[\frac{d}{dx} f(g(h(k(...(x)))))=f'()~g'()~h'()~k'()~.......x'\]
anonymous
  • anonymous
wait what i dont get it..

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perl
  • perl
amistre is showing off :D
anonymous
  • anonymous
@amistre64
anonymous
  • anonymous
@perl can u help?
amistre64
  • amistre64
all this amounts to is chain rule practice .... if you know the chain rule, then its just a matter of keeping a clean record
perl
  • perl
amistre, i dont thats right though
perl
  • perl
|dw:1366900627282:dw|
anonymous
  • anonymous
ok so im new to this ..can u teach me pls?
amistre64
  • amistre64
there are some cases where the mechanism of a derivative works, but the equation itself is bad .... i dont think this is the case tho
anonymous
  • anonymous
what do u want me to do?
anonymous
  • anonymous
:O
perl
  • perl
|dw:1366900684785:dw|
amistre64
  • amistre64
y= tan(cos(e^sqrt(x^2+1))) let: f = tan(g) g= cos(h) h = e^j j = sqrt(k) k = x^2+1
anonymous
  • anonymous
ok..
amistre64
  • amistre64
then find the derivative of each one, and multiply them all together ...
anonymous
  • anonymous
but hw can i take derivative of tan(g)(h)(j)(k) ?
amistre64
  • amistre64
take the derivative of f take the derivative of g take the derivative of h ... NOT take the derivative of f tan(g)(h)(k)...
anonymous
  • anonymous
ok so i go backwards?
amistre64
  • amistre64
let: f = tan(g) f' = ??? g= cos(h) g' = ??? h = e^j h' = ??? j = sqrt(k) j' = ??? k = x^2+1 k' = ???
amistre64
  • amistre64
take them one at a time
anonymous
  • anonymous
ok..so k'=2x and j'= 1/x^1/2 rite?
amistre64
  • amistre64
correct
amistre64
  • amistre64
except use the "variable" as in each case; only the last one uses an x
amistre64
  • amistre64
let: f = tan(g) f' = sec^2(g) g= cos(h) g' = -sin(h) h = e^j h' = j e^j j = sqrt(k) j' = 1/(2sqrt(k)) k = x^2+1 k' = 2x
anonymous
  • anonymous
ok can u wait fr a few moments..ill try solving the whole thing and tell u the answer so u can tell me if its right or wrong?
amistre64
  • amistre64
i would personally leave it in a "defined" format so that it is cleaner to write up
anonymous
  • anonymous
but tom i have an exam..so there i cant keep it clean..i have 2 give the answer..so ill solve it..would u pls pls check it?
amistre64
  • amistre64
ill chk it when your done ....
anonymous
  • anonymous
wait..fr e^j shouldnt it be e^j * d/dx of j?
amistre64
  • amistre64
hmmm, j' e^j yes, but your already solving for j' so thats really just e^j
amistre64
  • amistre64
the j' is part of the chain rule process, which you are already doing ....
amistre64
  • amistre64
good eye :)
anonymous
  • anonymous
:D thnx...fr ure help also.. :)

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