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## anonymous 5 years ago 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

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1. anonymous

Do you mean find dw/dt where$w=\frac{xe^y}{z}, x=t^6, y=9-t, z=4+4t?$

2. anonymous

yes

3. anonymous

i got an answer I keep on getting the same one, but my hw is online and it marks it wrong

4. 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$\frac{dw}{dt}=\frac{dw}{dx}(\frac{dx}{dt}\frac{dt}{dy})(\frac{dy}{dt}\frac{dt}{dz})\frac{dz}{dt}$

5. anonymous

this is for calc 3 so I have to multiply the leibniz notation and add them

6. anonymous

Ah, okay, knowing the level helps.

7. 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.

8. anonymous

yes I have computed that

9. anonymous

I'm doing the rest...

10. anonymous

hey lokisan do you get the divisible sign to be straight instead of this /

11. anonymous

I get $\frac{dw}{dt}=\frac{-4t^6}{(4+4t)^2}e^{9-t}$

12. anonymous

Did you need just a check on your answer, or the full-on working?

13. anonymous

nadeem, you type "frac{}{}" into the equation editor. Your numerator and denominator go in the first and second parentheses respectively.

14. anonymous

that's wassup..... appreciate it

15. anonymous

no probs

16. anonymous

is that what you get? how did you get that?

17. anonymous

Just doing what each derivative asks of me first$\frac{dw}{dt}=(\frac{e^y}{z}).t^6+\frac{xe^y}{z}.(-1)+(-\frac{xe^y}{z^2}).4$

18. 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.

19. anonymous

This is what I got: $\frac{dw}{dt}=\frac{-4t^5e^{9-t}(t^2-4t-6)}{(4+4t)^2}$

20. anonymous

$\frac{dw}{dt}=(\frac{e^{9-t}}{4+4t}).t^6-\frac{t^6e^{9-t}}{4+4t}-4\frac{t^6e^{9-t}}{(4+4t)^2}$

21. anonymous

The first two parts cancel, the third is left over.

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