`d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))]=` `1/(2(1+x)sqrt(x))` (b) `3/((1+x)sqrt(x))` `2/((1+x)sqrt(x))` (d) `3/(2(1+x)sqrt(x))`

Options

A. `(2(1-(3sqrt(3))/(4)), (3)/(2) (1-(4)/(sqrt(3))))`
B. `(-2(1+sqrt(3)), (3)/(2) (1-sqrt(3)))`
C. `(2(1+sqrt(3)), (3)/(2) (1+sqrt(3)))`
D. `(2(1+(3sqrt(3))/(4)), (3)/(2) (1+(4)/sqrt(3)))`

Answer

A, D

Explanation

AB =5, `D-=(2,(3)/(2))`
`CD = 5 xx (sqrt(3))/(2) = (5sqrt(3))/(2)`
`"Slope of AB" =-(3)/(4)`
Slope of CD `=(3)/(4)`
If `C-=(h,k), "then"`
`(h-2)/(3//5) = (k-3//2)/(4//5) = +-(5sqrt(3))/(2)`
`"or " h=2(1-(3sqrt(3))/(4)), k=(3)/(2)(1-(4)/(sqrt(3)))`
`"or " h=2(1+(3sqrt(3))/(4)), k=(3)/(2)(1+(4)/(sqrt(3)))`