If `f'(x)=sin(log x)and y=f((2x+3)/(3-2x)),` then `dy/dx` equals

Options

A. `6 sin log(5)`
B. `5 sin log(6)`
C. `12 sin log(5)`
D. `5 sin log (12)`

Answer

C

Explanation

`(dy)/(dx)=f((2x+3)/(3-2x))d/(dx)((2x+3)/(3-2x))`
`=sinlog((2x+3)/(3-2x))`
`(((3-2x)(2)-(2x+3)(-2))/((3-2x)^(2)))`
`=12/((3-2x)^(2))sin{log((2x+3)/(3-2x))}`
`:.((dy)/(dx))_(x=1)=112/((3-2)^(2))sin log 5`
`=12sin log5`