marytheshade 3 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. frx

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

2. frx

Then you just replace the derivitives using the chainrule

3. frx

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

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. frx

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

6. frx

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

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. frx

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. Chlorophyll

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

Thank you!!

11. frx

np