यदि `y = tan^(-1) ((5-2 tan sqrt(x))/(2 + 5 tan sqrt(x)))` है, तो `(dy)/(dx)` किसके बराबर है ?

Options

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

Explanation

दिया है,
`y = tan^(-1) ((5-2tansqrt(x))/(2+5tansqrt(x)))`
`y = tan^(-1) ((5/2-tansqrt(x))/(1+5/2 tansqrt(x)))`
माना `5/2 = tan A`
`= tan^(-1) ((tanA' - tansqrt(x))/(1+tanAtansqrt(x)))`
`= tan^(-1) [tan (A - sqrt(x))]`
`= A - sqrt(x)`
`y = tan^(-1) 5/2 - sqrt(x)`
x के सापेक्ष अवकलन करने पर,
`(dy)/(dx) = (-1)/(2sqrt(x))`