Differentiation Question?

Question

Differentiate the following:

F(t) = ln ((2t+1)^3/(3t-1)^4)

please show all working out and formulas used thanks in advance

Answer 1

ln(u)=du/u

d(((2t+1)^3/(3t-1)^4))
let
u=(2t+1)^3
then du=3(2t+1)^2(2)=6(2t+1)^2
v=(3t-1)^4
then
dv=4((3t-1)^3)3

d(u/v)=(vdu-udv)/v2 by chuain rule


u substitute the variable and simpify it to get the answer.

Answer 2

F'(t)={(2t+1)^3/(3t-1)^4}'/{(2t+1)^3/(3t-1)^4]

= {3*2* (2t+1)^2 * (3t-1)^4 -( 4*3*(3t-1)^3 *((2t+1)^3) }
over {(2t+1)^3/(3t-1)^4}

hint: (ln u)' = (u)'/ u

(u / v)' =(u' v - v' u) / v^2

Answer 3

ans is {-8t^3+8t^2+19t+6}/(t-1)