Question

d/dx tan⁻¹ 1-x/1+x=........,Select Proper option from the given options.
(a) - 1/1+x²
(b) 1/1+x²
(c) 1+x/1-x
(d) 2/1+x²

Answer 1

In the attachment I have answered this problem.         I have applied chain rule and quotient    rule to find  derivative of the given function.           See the attachment for detailed solution.

Answer 2

we have to find the value of d{tan^-1(1-x)/(1+x)}/dx

d{tan^-1(1-x)/(1+x)}/dx = 1/[1 + {(1-x)/(1 + x)}²] × d{(1 - x)/(1 + x)}/dx

= (1 + x)²/[(1 + x)² + (1 - x)²] × [(1 + x)(-1) - (1 - x)]/(1 + x)²]

= (1 + x)²/[1 + x² + 1 + x²] × [-2/(1 + x)²]

= -(1 + x)²/{2(1 + x²) } × 2/(1 + x)²

= -1/(1 + x²)

hence, option (a) is correct.