## anonymous 4 years ago I need to find the derivative using the chain and quotient rules of F(x)= ((3x-2)^3)/((x-3)^5). I just don't know when to stop doing chain rule and start the quotient

1. anonymous

Start by thinking of the quotient rule, it's (f'(x)g(x)-f(x)g'(x))/(g(x))^2

2. anonymous

Then you just replace the derivitives using the chainrule

3. anonymous

$\frac{ f'(x)*(x-3)^{5} - (3x-2)^{3}g'(x) }{(x-3)^{10} }$

4. anonymous

don't you have to do the chain rule first? is it possible to derive the F(x) and g(x) equations without the chain rule?

5. anonymous

You have to do the chainrule when replacing the derivitives in the function i wrote above

6. anonymous

I think it's easier to start of writing it as above

7. anonymous

okay so I did the chain rule and got F'(g(x))= 9(3x-2)^2 (top function deriv) and g'(x)= 5(x-3)^4 (denominator deriv) so do I plug in those values or do I have to take the chain rule further?

8. anonymous

You just put them in as you counted them, the derivitive of f(x) is f'(x) and it's what you're looking for according to the quotientrule.

9. anonymous

You've done with derivative u' and v' Plug them into the formula ( u'v - uv' ) / v²

10. anonymous

Thank you!!

11. anonymous

np