`(d)/(dx){:[tan^(-1)((sqrt(x)(3-x))/(1-3x))]:}` का मान होगा

Options

A. `(1)/(2(1+x)sqrt(x))`
B. `(3)/((1+x)sqrt(3))`
C. `(2)/((1+x)sqrt(3))`
D. `(3)/(2(1+x)sqrt(x))`

Answer

D

Explanation

मान लीजिए `y=tan^(-1){(3sqrt(x)-x^(3//2))/(1-3x)}`
`sqrt(x)=tant` रखने पर,
`y=tan^(-1){(3tant-tan^(3)t)/(1-3tan^(2)t)}`
`=tan^(-1)(tan3t)=3t`
`rArr" "y=3tan^(-1)sqrt(x)`
`:." "(dy)/(dx)=(3)/(1+x)(1)/(2sqrt(x))=(3)/(2(1+x)sqrt(x))`