Question

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

Answer 1

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

Answer 2

Then you just replace the derivitives using the chainrule

Answer 3

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

Answer 4

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?

Answer 5

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

Answer 6

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

Answer 7

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?

Answer 8

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.

Answer 9

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

Answer 10

Thank you!!

Answer 11

np