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1)

If y= (tan1x)2 , then

 (x2+1)2d2ydx2+2x(x2+1)dydx=


A) 4

B) 2

C) 1

D) 0

Answer:

Option A

Explanation:

We have   y= (tan1x)2

 on differentiating  w.r.t x, we get

dydx=2tan1x1+x2

     (1+x2)dydx=2tan1x

 On squaring both sides, we get

(1+x2)2(dydx)2=4(tan1x)2

     (1+x2)2(dydx)2=4y       [y=tan1x)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