Question

can I use Another Method other then UV method to differentiating this question ​

Answer 1

yes we can differentiate by another method

let Y= x³/(3x-2)

taking log

log Y= log x³-log( 3x-2)

diff w r t x

1/Y dy/dx= 3/x- 3/(3x-2)

dy/dx= [ 3/x-3/(3x-2)]× Y

putting the value of Y

dy/dx= x³)[ 3/x-3/(3x-2) ] / (3x-2)

= 3x³[ 1/x- 1/(3x-2)] /( 3x-2)

= 3x³[ (3x-2-2x) / x( 3x-2]/ (3x-2)

= 3x³[ (2x-2)/ x(3x-2)] /(3x-2)

= 6x³[ ( x-1)/ x( 3x-2)² ]

= 6x²(x-1) / ( 3x-2)²

this is the final answer