I'm using the chain rule and i need to find the derivative of Y=((3x-2)/(6-5x))^4

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I'm using the chain rule and i need to find the derivative of Y=((3x-2)/(6-5x))^4

Mathematics
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do you know how to find the derivative of \[\frac{3x-2}{6-5x}\]?
that is all the hard work.

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

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