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

1. Owlfred

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2. anonymous

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

3. anonymous

that is all the hard work.

4. 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.

5. anonymous

i can write it for you if you like

6. anonymous

hello anwar. feel like writing it out?

7. 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!!

8. anonymous

hello satellite :)

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

Oh the whole thing.. my bad.

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

Yeah.

17. anonymous

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

18. anonymous

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

19. anonymous

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

20. anonymous

bet we lost doshi somewhere

21. anonymous

probably gave up in disgust

22. anonymous

I think so :D