If y=tan-1x1-x2, then dydx=
-11-x2
x1-x2
11-x2
1-x2x
Explanation for the correct option.
Find the value of dydx.
Let x=sinθ, then θ=sin-1x
In the equation y=tan-1x1-x2, substitute sinθ for x.
y=tan-1sinθ1-(sinθ)2=tan-1sinθcos2θ∵sin2A+cos2A=1=tan-1sinθcosθ=tan-1tanθ=θ
But θ=sin-1x, so the value of y=sin-1x.
Now differentiate it with both sides with respect to x.
dydx=ddxsin-1x=11-x2
Hence, the correct option is C.