If ` y = tan^(-1) ((4sqrt(x))/(1 - 4x))" then" (dy)/(dx)` is

Options

A. `(2^(x)log 2)/(1 + 4^(x))`
B. `(2^(x)log 8)/(1 + 4^(x))`
C. `(2^(x)log 4)/(1 + 4^(x))`
D. None of the above

Answer

C

Explanation

Given , ` y = tan^(-1) ((2.2^(x))/(1 - (2^(x)))) `
Put ` tan^(-1) ((2tan theta)/(1 - tan^(2) theta))= tan^(-1) (tan 2 theta)`
` = 2 theta = 2 tan^(-1) 2^(x)`
`(dy)/(dx) = (2)/(1 + (2^(x))^(2)). 2^(x) . Log 2 = (2^(x) log 4)/( 1 + 4^(x))` .