DIFFERENTIATION doubt

Q1) y=tan-1[âˆš1+x2 + âˆš1-x2 /âˆš1+x2 - âˆš1-x2], then dy/dx=?
a) 1/âˆš1-x4
b) -1/âˆš1-x4
c) x/âˆš1-x4
d) -x/âˆš1-x4

2 Answers

observe
its tan^-11+tan^-1(√1-x²/√1+x²).

Answer is d

first of all rationalize stuff inside the tan inverse function.
this will get you tan^-1(1+√1-x⁴x²)

now assume cos2z = x
By applying trigonometry now, you may reach
tan^-1 ( 1+tanz1-tanz)
which is equal to tan^-1(tan 45 + z)

which is equal to 45 degrees + z
now put z = cos^-1x²2

differentiating now.....we get d as the answer

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