Answer:
Option A
Explanation:
We have y= (tan−1x)2
on differentiating w.r.t x, we get
dydx=2tan−1x1+x2
⇒ (1+x2)dydx=2tan−1x
On squaring both sides, we get
(1+x2)2(dydx)2=4(tan−1x)2
⇒ (1+x2)2(dydx)2=4y [∵y=tan−1x)2]
Again , differentiating w.r.t x , we get
(1+x2)2(2dydx.d2yd2x)+2(1+x2)(2x)(dydx)2=4dydx
On dividing both sides by 2dydx,
we get
(1+x2)2(d2yd2x)+2x(1+x2)dydx=4