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

Question

owlfred · Answer

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anonymous · Answer

do you know how to find the derivative of $$\frac{3x-2}{6-5x}$$?

anonymous · Answer

that is all the hard work.

anonymous · Answer

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 · Answer

i can write it for you if you like

anonymous · Answer

hello anwar.  feel like writing it out?

anonymous · Answer

$${d \over dx}({3x-2 \over (6-5x)^4})={3(6-5x)-4(3x-2)(6-5x)^3(-5) \over (6-5x)^8}$$
Simplify!!

anonymous · Answer

hello satellite :)

anonymous · Answer

ok i will.  i get $$\frac{8}{(5x-6)^2}$$

anonymous · Answer

The denominator is raised to the power of 4, isn't it?

anonymous · Answer

so back to the problem.  the derivative will be 
$$4(\text{inside thing})^3\times \frac{8}{(5x-6)^2}$$

anonymous · Answer

Oh the whole thing.. my bad.

anonymous · Answer

no i was assuming it was the whole thing raised to the 4th.  chain rule and all that.

anonymous · Answer

never mind my solution doshi, just stick with satellite :D

anonymous · Answer

inside piece just $$\frac{3x-2}{5x-6}$$

anonymous · Answer

Yeah.

anonymous · Answer

well actually it is 
$$\frac{3x-2}{6-5x}$$

anonymous · Answer

whose derivative is $$\frac{3(6-5x)+5(3x-2)}{(5x-6)^2}=\frac{8}{(5x-6)^2}$$

anonymous · Answer

The derivative 
$$y'=4({3x-2 \over 6-5x})^3{8 \over (6-5x)^2}$$

anonymous · Answer

bet we lost doshi somewhere

anonymous · Answer

probably gave up in disgust

anonymous · Answer

I think so :D