anonymous
  • anonymous
Use the Chain Rule to find dw/dt. (Enter your answer only in terms of t.) w = xey /z, x = t6, y = 9 - t, z = 4 + 4t
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Do you mean find dw/dt where\[w=\frac{xe^y}{z}, x=t^6, y=9-t, z=4+4t?\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
i got an answer I keep on getting the same one, but my hw is online and it marks it wrong

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anonymous
  • anonymous
OK. If you really *must* use the chain rule to solve,\[\frac{dw}{dt}=\frac{dw}{dx}\frac{dx}{dy}\frac{dy}{dz}\frac{dz}{dt}\]Then expand dx/dy and dy/dz again\[\frac{dw}{dt}=\frac{dw}{dx}(\frac{dx}{dt}\frac{dt}{dy})(\frac{dy}{dt}\frac{dt}{dz})\frac{dz}{dt}\]
anonymous
  • anonymous
this is for calc 3 so I have to multiply the leibniz notation and add them
anonymous
  • anonymous
Ah, okay, knowing the level helps.
anonymous
  • anonymous
Well, in that case, it's just\[\frac{dw}{dt}=\frac{dw}{dx}\frac{dx}{dt}+\frac{dw}{dy}\frac{dy}{dt}+\frac{dw}{dz}\frac{dz}{dt}\] where all the 'd's are partial.
anonymous
  • anonymous
yes I have computed that
anonymous
  • anonymous
I'm doing the rest...
anonymous
  • anonymous
hey lokisan do you get the divisible sign to be straight instead of this /
anonymous
  • anonymous
I get \[\frac{dw}{dt}=\frac{-4t^6}{(4+4t)^2}e^{9-t}\]
anonymous
  • anonymous
Did you need just a check on your answer, or the full-on working?
anonymous
  • anonymous
nadeem, you type "frac{}{}" into the equation editor. Your numerator and denominator go in the first and second parentheses respectively.
anonymous
  • anonymous
that's wassup..... appreciate it
anonymous
  • anonymous
no probs
anonymous
  • anonymous
is that what you get? how did you get that?
anonymous
  • anonymous
Just doing what each derivative asks of me first\[\frac{dw}{dt}=(\frac{e^y}{z}).t^6+\frac{xe^y}{z}.(-1)+(-\frac{xe^y}{z^2}).4\]
anonymous
  • anonymous
Then substitute each of the x=t^6, y=... into the above. You should find that the first two quotients cancel out, and you're left with the last quotient -> the answer.
anonymous
  • anonymous
This is what I got: \[\frac{dw}{dt}=\frac{-4t^5e^{9-t}(t^2-4t-6)}{(4+4t)^2}\]
anonymous
  • anonymous
\[\frac{dw}{dt}=(\frac{e^{9-t}}{4+4t}).t^6-\frac{t^6e^{9-t}}{4+4t}-4\frac{t^6e^{9-t}}{(4+4t)^2}\]
anonymous
  • anonymous
The first two parts cancel, the third is left over.

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