If x=y(1-y2), then dydx is equal to
x
1-y21+2y2
0
1-y21-2y2
Explanation for the correct option.
x=y(1-y2)
Differentiate w.r.t x
1=y-2y21-y2dydx+1-y2dydx⇒1=y-2y21-y2+1-y2dydx⇒1=-y2+1-y21-y2dydx⇒1=1-2y21-y2dydx⇒dydx=1-y21-2y2
Hence, option D is correct.