Question

What is the derivative of:

f(x) = (3x+1)^3 / (1-3x)^4

I get (3x+1)^2 (9x+21) / (1-3x)^5

Answer 1

(3x+1)^3 (1-3x)^-4

9(3x+1)^2 12(3x+1)^3
--------- + ------------
(1-3x)^4 (1-3x)^5

Answer 2

(1-3x) 9(3x+1)^2 12(3x+1)^3
----- --------- + ------------
(1-3x) (1-3x)^4 (1-3x)^5


(9-27x) (3x+1)^2 + 12(3x+1)^3
-----------------------------
(1-3x)^5

is what I get if we split it and use the product rule

Answer 3

By quotient I get:


(1-3x)^4 9(3x+1)^2 - (-12)(1-3x)^3 (3x+1)^3
-------------------------------------------
(1-3x)^8



(1-3x)^3 [(1-3x) 9(3x+1)^2 + 12(3x+1)^3 ]
------------------------------------------
(1-3x)^3 (1-3x)^5


9(1-3x)(3x+1)^2 + 12(3x+1)^3
-----------------------------
(1-3x)^5


(9-27x)(3x+1)^2 + 12(3x+1)^3
----------------------------
(1-3x)^5

................same thing

Answer 4

Thanks, I see where I messed up