anonymous
  • anonymous
I'm using the chain rule and i need to find the derivative of Y=((3x-2)/(6-5x))^4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Owlfred
  • Owlfred
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anonymous
  • anonymous
do you know how to find the derivative of \[\frac{3x-2}{6-5x}\]?
anonymous
  • anonymous
that is all the hard work.

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anonymous
  • anonymous
then the "chain rule" will tell you that since this is something to the power of 4, its derivative will be 4 something cubed times the derivative of something. so all the work is finding the derivative of that quotient.
anonymous
  • anonymous
i can write it for you if you like
anonymous
  • anonymous
hello anwar. feel like writing it out?
anonymous
  • anonymous
\[{d \over dx}({3x-2 \over (6-5x)^4})={3(6-5x)-4(3x-2)(6-5x)^3(-5) \over (6-5x)^8}\] Simplify!!
anonymous
  • anonymous
hello satellite :)
anonymous
  • anonymous
ok i will. i get \[\frac{8}{(5x-6)^2}\]
anonymous
  • anonymous
The denominator is raised to the power of 4, isn't it?
anonymous
  • anonymous
so back to the problem. the derivative will be \[4(\text{inside thing})^3\times \frac{8}{(5x-6)^2}\]
anonymous
  • anonymous
Oh the whole thing.. my bad.
anonymous
  • anonymous
no i was assuming it was the whole thing raised to the 4th. chain rule and all that.
anonymous
  • anonymous
never mind my solution doshi, just stick with satellite :D
anonymous
  • anonymous
inside piece just \[\frac{3x-2}{5x-6}\]
anonymous
  • anonymous
Yeah.
anonymous
  • anonymous
well actually it is \[\frac{3x-2}{6-5x}\]
anonymous
  • anonymous
whose derivative is \[\frac{3(6-5x)+5(3x-2)}{(5x-6)^2}=\frac{8}{(5x-6)^2}\]
anonymous
  • anonymous
The derivative \[y'=4({3x-2 \over 6-5x})^3{8 \over (6-5x)^2}\]
anonymous
  • anonymous
bet we lost doshi somewhere
anonymous
  • anonymous
probably gave up in disgust
anonymous
  • anonymous
I think so :D

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